Question

Solve for x. Round your answer to two decimal places. Show your work for full credit. (3 points) A right triangle is shown with the hypotenuse labeled x. One angle has a measure of thirty nine degrees, and the opposite leg has a length of nine.

Answer 1

Answer:

$x = 14.30$

Step-by-step explanation:

Given:

Right ∆ with,

Hypotenuse = x

Opposite = 9

Reference angle $\theta$ = 39°.

Required:

The value of x

Solution:

Since we are given a reference angle with opposite length, and we are to find the hypotenuse length, x, apply the following trigonometric ratios formula:

$sin(\theta) = \frac{opp}{hyp}$

Plug in the values into the equation

$sin(39) = \frac{9}{x}$

Multiply both sides by x

$sin(39)*x = 9$

Divide both sides by sin(39)

$x = \frac{9}{sin(39)}$

$x = 14.30$ (to 2 decimal places)