Answered: Refer to right triangle ABC with C =…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter5: Similar Triangles

Section5.CT: Test

Problem 6CT: In right triangle ABC,CD- is the altitude from C to hypotenuse AB-. Name three triangles that are...

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Refer to right triangle ABC with C = 90°. Begin each problem by
drawing a picture of the triangle with both the given and askedfor information labeled
appropriately. Also, write your answers for angles in decimal degrees.

If b=2.7 m and c = 7.7 m , find A

Expert Solution

Step 1

Given right angled triangle $A B C$ with $C = 90 °$ .

Also, given that $b = 2.7$ m and $c = 7.7$ m.

To find: $∠ A$

Solution:

The diagram will be:

Step 2

We have $A C = 2.7 m, A B = 7.7 m$ .

Using Pythagoras theorem,

$\begin{array}{rcl} {(A B)}^{2} & = & {(A C)}^{2} + {(B C)}^{2} \\ {(7.7)}^{2} & = & {(2.7)}^{2} + {(a)}^{2} \\ a & = & \sqrt{{(7.7)}^{2} - {(2.7)}^{2}} \\ a & = & \sqrt{59.29 - 7.29} \\ a & = & \sqrt{52} \\ a & = & 7.21 \end{array}$

From cosine rule of triangle, we have

$\begin{array}{rcl} \cos A & = & \frac{b^{2} + c^{2} - a^{2}}{2 b c} \\ \cos A & = & \frac{b^{2} + c^{2} - a^{2}}{2 b c} \\ \cos A & = & \frac{{(2.7)}^{2} + {(7.7)}^{2} - {(7.21)}^{2}}{2 (2.7) (7.7)} \\ \cos A & = & \frac{66.58 - 52}{41.58} \\ \cos A & = & \frac{14.58}{41.58} \\ \cos A & = & 0.350 \\ A & = & 69.51 ° \end{array}$

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