3. Let a = -i+ 3j + 2k and b = 4i + 5j+ 2k. Don’t evaluate the square roots for the lengths except when evaluating the angle in part (c). (a) Determine the length of a in the direction of b.

Q: 4. If a golfer uses a 64° wedge, he will send the ball into the air at an angle of 64°. He is…

A: As per given question  Will he be able to hit the ball over the tree?

Q: Find the angle formed by two face diagonals that intersect at a vertex of the cube.

A:

Q: Suppose that Tis a point on side PQ of APQR. Also, RT bisects ZPRQ, and ZP = 2Q. If Z1 and 2 are the…

A: Consider triangle PQR, As RT bisect angle R, ∠PRT=∠QRT Given that ∠P=∠Q ∠RTP=∠1∠RTQ=∠2

Q: 2. Explain why Corollary 2 is true. That is, explain how the fact that MXN is a semicircle leads to…

A: We have given information that MXN⏜ is a semicircle so,  MN is the diameter  given figure is

Q: Find the Hhe Teast square doluticn E of -6 -7 La %3D ->

A: From A we can write AT = 100010 ATA = 100010100100 = 1001

Q: What is the sum of the exterior angles of a pentagon?

A: Here we want to find sum of exterior angles 9f Pentagon.

Q: Show that the points (a,a),(-a,-a) and (-V3a, v3a) are the За vertice of an equilateral triangle.…

A: Given the co-ordinate of a triangle Let A=(a,a)B=(−a,−a)C=(−3a,3a)

Q: 5A. In quadrilateral ABCD, ∠B=∠D, ∠B= (2x+5)°, ∠A=3x and x=35°, prove that ABCD is a parallelogram.

A: We need to prove that ABCD is parallelogram.

Q: In ASTU, u = 23 inches, ZT=158° and ZU=17°. Find the length of t, to %3D the nearest 10th of an…

A: Given: - In ∆STU, u=23 inches, ∠T=158° and ∠U=17°. To find: - The length of t, to the nearest 10th…

Q: Try to move the purple points of Parallelogram ABCD so that the midpoints of AC & BD are different.…

A: In a parallelogram the diagonals bisect each other i.e. the midpoints are same point.

Q: C В A In the figure above AB = 4x +6 and BC = 7x + 15. If AC 120, find the length of segment AB. %3D…

A:

Q: Consider this right triangle. 17 30° Enter the value of side length x.

A: We can find the value of x as below

Q: 15. Max built a skateboarding ramp that is 16 inches high. The angle formed by the ramp and the…

A: Here we use trigonometry to find length of ramp.

Q: use the isosceles right triangle in Figure 6.4. Express your answers in simplest radical form. If b…

A:

Q: Give the theorem that supports the similarity of the given pairs of triangles. Then find the length…

A: Give the theorem that supports the similarity of the given pairs of triangles. Then find the length…

Q: An airplane is approaching Los Angeles International Airport at an altitude of 2,640 feet. If the…

A:

Q: 2. What is the angle 0 between the straight lines AB and AC?

A:

Q: 4. Find OQ. Explain. 0Q = parallelogram because MNOP is a parallelogram and the each other, so MQ =…

A: Given MNOP is Parallelogram and x=4. We Know that the Diagonals in a parallelogram bisect each…

Q: In Hyperbolic Geometry, the sum of internal angles of a triangle is always greater than 180°. True…

A: False

Q: 16) 28 20

A:

Q: Find a positive angle less than 2π that is coterminal with a -π/15 angle ?

A: the angle less than 2π is in the first and second quadrant and coterminal angles repeat after…

Q: Express the result in trigonometry and rectangular form 1 43. (1 + V3i)6

A: D-Moivre's theorem: If z=reiθ, then it is a complex number. Then, zn=rn(cosnθ+isinnθ) where n is…

Q: an equilateral triangle has sides of the length 2x+48, 103-3x and 6x+4. What is x?

A: an equilateral triangle has sides of the length 2x+48, 103-3x and 6x+4. What is x?

Q: Select the procedure that can be used to show the converse of the Pythagorean theorem using side…

A:

Q: The sides of the pair of angles are parallel. Are 23 and Z4 congruent? 3

A: Given, the sides of the pair of angles are parallel.

Q: Can you use the angle bisector theorem to solve for mZWYZ?

A: Given Data: The length of side XW is: XW=9 The length of side ZW is: ZW=9 The measure of angle XYW…

Q: Your friend claims that the SAS Congruence Theorem (Theorem 5.5) will apply to a triangle and its…

A: We know by the SAS congruence theorem Two sides and the included angle of one triangle are…

Q: The coordinates at the vertices.A.B, and C of the triangle ABC are (-3,7), (2,19), and (10,7)…

A: Given,  The coordinates of vertices of triangle A-3, 7  B2, 19  C10, 7   We have to find the length…

Q: 4. AB intersects CD at E. If the mLAEC is 8x- 15 and mLAED is 9x + 76, find all the angles.

A:

Q: 10x 4x – 1 5x 10x 10x 3x +1 2x +3 F 10x

A:

Q: CONSTRUCT EQUILATERAL TRIANGLE UPON AB AS THE BASE. At

A: According to question given thatAB is the base of the equilateral triangle and we have to construct…

Q: On a piece of paper, use your protractor to draw a triangle that has two angles of the same measure.…

A: We will take a piece of paper, By using our protractor to draw a triangle that has two angles of…

Q: Angelo is fencing off an area against the side of his warehouse. In the diagram below, you can see…

A:

Q: be a right triangle. Which

A:

Q: Classify AABC by its angles if mZA = x, mZB=2x , and m/C = 3x. right isosceles equilateral obtuse

A: By using property of triangle

Q: An altitude of an equilateral triangle has length 6\/3 . What is the perimeterof the triangle?

A: An altitude of an equilateral triangle has length 63. What is the perimeterof the triangle?…

Q: Find angle NFE * M²GFN = 4x+ 10, mZNFE = 14x + 3, %3D %3D and mzGFE = 157°. Find mNFE. N

A: Given that,∠GFE = 157°WE HAVE TO FIND ∠NFE

Q: Can you use the angle bisector theorem to solve for QT?

A: Given,

Q: How would you use the distance formula to show that a parallelogram is a rectangle?

A: In case of parallelogram ABCD given below, It can be proven using distance formula that, AB=CD and…

Q: 2) Point B is the midpoint of AC. If AB=3x, BC=2x+2, what is the length of AC?

A:

Q: If RS = 40, ST = 41, and RT = 11, is ARST a right triangle? Explain. %3D %3D %3D

A: Check by Pythagorean theorem

Q: Consider a right triangle with a side of length x opposite angle A, a side of length y opposite…

A:

Q: use the isosceles right triangle in Figure 6.4. Express your answers in simplest radical form. If c…

A:

Q: A B 29 сm 16 сm 10cm

A: We know,  tan θ = opposite sideadjacent side

Q: Prove analytically that the perpendicular bisector of the sides of a triangle are concurrent.

A:

Q: A right triangle has legs of length X, 2X +2, and a hypotenuse of length 2X +3. What are the Lengths…

A: Topic: triangle

Q: Sketch in standard position on a grid below the angles 5pi/3(as a solid line) and -2pi/3(as a dashed…

A:

Q: The length of a diagonal of a square whose side is 4 in. long. Leave answer in simplified radial…

A: SQUARE: A Square is a Quadrilateral that has Four Equal Sides Each angle at the corner are of 90°…

Q: What is the measure of the angle between the diagonal of a cube and the diagonal of the face of the…

A: Let's take 1,1,1 as the body diagonal vector b Let's take 1,1,0 as the face diagonal vector f Let's…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.