Question

What is the length of Line segment A B? Round to the nearest tenth. Triangle A B C is shown. Angle A C B is a right angle and angle C A B is 75 degrees. The length of C A is 10 meters and the length of hypotenuse A B is x. 9.7 m 10.4 m 37.3 m 38.6 m

Answer 1

Answer:

D.) 38.6 m

Step-by-step explanation:

Use the cosine ratio:

$cosine=\frac{adjacent}{hypotenuse}$

Because we are given the measure of an angle and the length next to it (adjacent), and we need to find the hypotenuse (the hypotenuse is NEVER considered the adjacent side). Insert the values:

$cos75=\frac{10}{x}$

Now isolate the variable. Multiply both sides by x:

$x(cos75)=x(\frac{10}{x} )$

The x's on the right side cancel each other out. Simplify:

$x*cos75=10$

Now divide both sides by cos75°:

$\frac{x*cos75}{cos75} =\frac{10}{cos75}$

The cos75° on the left side cancels each other. Simplify:

$x=\frac{10}{cos75}$

Insert this value into a calculator to simplify the value of x:

$x=38.6$

The hypotenuse is 38.6 m.

:Done