The length of the hypotenuse of a 30°-60°-90° triangle is 4. Find the length opposite to 60° angle

Q: The diagonals of a parallelogram are 14 meters and 16 meters and intersect at an angle of 60°. Find…

A: Given the diagonals of a parallelogram are 14 m and 16 m. Diagonals intersect at an angle of 60°.

Q: Haley planted a new tree in her yard.  To help the tree to grow upright, she attached support wires…

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Q: From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of…

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Q: A right triangle has a 45 degree angle. The hypotenuse is twelve. What is the length of the other…

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Q: You are putting together the frame of a fence gate as shown below: If the width of the frame is 3…

A: We use Pythagoras theorem

Q: From a helicopter flying at 30,000 feet, the angles of depression of two cities are 28 and 55. How…

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Q: if the hypotenuse of a 45, -45 and -90 degree triangle is 13, what is the length of one of the legs

A: Here the given right angle triangle having angles 45, 45, 90 Since the two angles of the given…

Q: Find the six trig values of (2, - 4) if it's a point on the terminal side of an angle in standard…

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Q: Each problem that follows refers to triangle ABC.    If A = 45 degree , B = 60 degree , and a = 12…

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Q: The Statue of Liberty is approximately 305 feet tall. If the angle of elevation of a ship to the top…

A: We have to find

Q: Which formula would you use to find the coordinates of a midpoint of a side of a triangle?

A: We have to find the formula for the coordinates of a midpoint of a side of a triangle?

Q: The hypotenuse of a right triangle is twice as long as one of the legs. How long is the other leg?…

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Q: Relative to the acute angle θ, the three sides of a right triangle are the ________ side, the…

A: Explanation: The longest side of the right triangle, which is also the side opposite the right…

Q: Solve the triangle b = 5, c = 3, A = 102°. Round lengths of sides to the nearest tenth and angle…

A: Explanation: Given that,  b=5 c=3 A=102° According to the cosine rule:…

Q: Use the fact that the longest side of a triangle is across from the largest angle to explain why the…

A: Here we have to prove that the hypotenuse is always the longest side in the right triangle.

Q: Find the measure of an angle that is twice as large as its supplement.

A: Given: Let the required angle be 2x and the supplement angle be x

Q: A straight kite string makes an angle of 40° with the ground, as shown in the diagram. If y = 210…

A: It is given that the length of the string is 210 feet  and angle of the string with the ground is…

Q: the railway is in the shape of an arch, at an angle of 28 . if the radius of the inner edge is…

A: To find- Difference in length of outer and inner edge.

Q: From a second storey of a building window directly across the street, the angle of elevation of the…

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Q: The hypotenuse of a right triangle is 12 feet. If one leg is 8 feet,find the degree measure of each…

A: Let ∆ABC be a right triangle. such that ∠B=90° To find: Measure of all angles.

Q: A broken flagpole forms a right triangle with the ground. If the angle which the broken part makes…

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Q: Gabe can see the top of the fountain by looking up at an angle of 39o . If Gabe is 1.3m tall and the…

A: Given that Gabe can see the top of the fountain at an angle of 39 degree. If Gabe is 1.3 m tall and…

Q: At a spot 400 feet from the base of a building the angle of elevation to the bottom of a flag pole…

A: To find height of flagpole

Q: Find the measures of the angles of the triangle whose vertices are A = (-1, 0), B = (2, 1), and C =…

A: The given three vertices of a triangle are A(-1,0), B(2,1) and C(1,-2). Now, considering the sides…

Q: If an angle in a right triangle is and the length of the opposite side to this angle is 18 cm, how…

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Q: Find the coordinates of the point on the unit circle at an angle of 3π/4

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Q: This problem refers to triangle ABC. If A=50 degrees, B=60 degrees, and b=10cm, find a.

A: Given,

Q: In a triangle, one angle is equal to 60" Find the obtuse angle formed by angle bisectors of the…

A: Considering triangle ABC, Given, Angle A= 60° Let the bisector of angle B and C meet at O.

Q: Solve triangle with b = 5, c = 3, A = 102°. Round lengths to the nearest tenth and angle measures to…

A: In triangle ABC - b = 5c = 3∠A = 102°Let's calculate the side a, using cosine formula on angle…

Q: find the length of the missing sides if side a is opposite angle A, side b is opposite angle B, and…

A: Solution : We have given that the length side of a = 10, side c is Hypotenuse and cosB = 4/5

Q: In the right triangle find the value of a to the nearest whole number if the hypotenuse is 20 m and…

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Q: From the top of a lighthouse 96 feet high, the angle of depression to a small boat is 37.1658°. How…

A: Follow the procedure given below.

Q: The measure of the angle 330° in standard position is given. Find two positive angles and two…

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Q: Solve the right triangle with a hypotenuse of 10 and an angle on 40 degrees

A: here we have the length of hypotenuse: AB=10 the length of the shorter leg: BC=x the length of the…

Q: Solve for the indicated angle 4x 113° 2x + 9° 3x + 8°

A: Topic = Geometry

Q: The height of an isosceles triangle is 6 cm. Find the third side if the length of the two aual sides…

A: Given, Height of an isosceles triangle =6 cm             the length of two equal sides  = 10 cm

Q: The bottom of a doorway to a building is 3.45 feet above the ground, and a ramp to the door for the…

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Q: From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of…

A: We know that the trigonometric ratio of tangent is  tan(x) = perpendicular / adjacent  tan(x) =…

Q: In the evening, a tree that stands 12 ft tall casts a shadow. If the angle of depression from the…

A: Consider the provided information, The graph is shown below, Find the length of the shadow.

Q: Side A has a length of 12 m, and angle Y is 12. What is the length of side B?

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Q: and

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Q: Brothers Bob and Tom Katz buy a tent that has a center pole 6.25 feet high. If the sides of the tent…

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Q: Write the Pythagorean theorem for a right triangle with the lengths of the legs given by a and b and…

A: Statement: Let a right angled triangle ABC, where B is right angled and we have to prove:

Q: Solve a right triangle that has a 40° angle and a 20 inch hypot

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Q: If triangle ABC is a right triangle with a = 20.5, b = 31.4, and C = 90 degree , solve thetriangle…

A: Given: a = 20.5, b = 31.4, and C = 90°

Q: If you stand 100 feet from the gym, how tall would it be if the angle of elevation feet to the top…

A: Lets assume that the gym is x feet tall . Drawing the Diagram as per  the Question , Let OA…

Q: Given a right triangle with a leg length of 7km and hypotenuse of length 25 km, find the length of…

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Q: Solve for all parts of the triangle when given a=17, b=18, and A=55 degree

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