Find the value of the variable. Round your answer to the nearest tenth

Question

asked Jan 11, 2021 176k views

2 Answers

Jason Braucht · Answer 1 · 2021-01-17T20:03:16+0000

Given:

The triangle DEF is a right triangle.

The length of EF is 12 units.

The length of DE is y units.

The measure of angle D is 25°

We need to determine the value of y.

Value of the variable:

The value of the variable y can be determined using the trigonometric ratio.

Thus, we have;

$tan \ \theta=(EF)/(DE)$

Substituting
$\theta=25^(\circ)$ , EF = 12 and DE = y, we get;

$tan \ 30^(\circ)=(12)/(y)$

Simplifying, we get;

$y=(12)/(tan \ 30^(\circ))$

y=(12)/(0.577)

y=20.797

Rounding off to the nearest tenth, we get;

y=20.8

Thus, the length of the variable y is 20.8 units.