Question

Find the value of t, rounded to the nearest tenth

Answer 1

Given:

Given that RST is a right triangle.

The measure of ∠R is 35°.

The length of ST is 12 units.

The length of the hypotenuse is t units.

We need to determine the value of t.

Value of t:

The value of t can be determined using the trigonometric ratio.

Thus, we have;

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

where $\theta=R$, the side opposite to ∠R is ST and hypotenuse is SR.

Substituting these values, we get;

$sin \ R=\frac{ST}{SR}$

Substituting ST = 12 and SR = t, we get;

$sin \ 35^{\circ}=\frac{12}{t}$

Simplifying, we get;

$t=\frac{12}{sin \ 35^{\circ}}$

$t=\frac{12}{0.574}$

$t=20.9$

Thus, the value of t is 20.9 units.