Question

For the triangle shown in the figure below what are each of the following? (Let y = 8.00 m and r = 10.0 m. Assume the triangle is a right triangle.)A diagram of a right triangle with a hypotenuse labeled r, one leg labeled x and the other leg labeled y. The angle adjacent to x is labeled and the angle adjacent to y is labeled .(a) the length of the unknown side x m(b) the tangent of (c) the sin of

Answer 1

Given a right angle triangle with:

y = 8.00 m

r = 10.0 m

(a) We are to find the length of the unknown side x?

Using pythagoras theorem:

r² = x² + y²

x² = r² - y²

x = √r² - y²

Inputting values:

x = √10² - 8²

x = √100 - 64

x = √36

x = 6 m

Therefore, the length of the unknow side x is 10 m.

(b) The tangent of θ

Using SOHCAHTOA

Tan θ = Opposite/Adjacent

Opposite = y = 8 m

Adjacent = x = 6

Tan θ = 8/6

Tan θ = 1.3

(c) Sin σ

Sin σ = Opposite/Hypotenuse

Opposite = x = 6 m

Hypotenuse = r = 10

Sin σ = 6/10

Sin σ = 0.6