Question

Given the sample triangle below and the conditions cosb=4/5, a=10 , find the hypotenuse of the triangle.

Answer 1

The measure of hypotenuses is 12.5 unit.

Explanation:

Given information:
`\cos b=(4)/(5), a=10`

In a right angle triangle

`\cos \theta=(base)/(hypoteneuose)`

Let the measure of hypotenuses be x.

In triangle ABC,

`\cos (B)=(CB)/(AB)`

`(4)/(5)=(10)/(x)`

`4* AB=10* 5`

`x=(50)/(4)`

`x=12.5`

Therefore the measure of hypotenuses is 12.5 unit.

Answer 2

See the attached figure
For the shown right triangle at C

cos B = a/c = a / hypotenuse
∵ cos B = 4/5 and a = 10

∴ 4/5 = 10/c
∴ c = 10/(4/5) = 10 * 5/4 = 12.5

∴ The hypotenuse of the triangle = 12.5