Question

1. determine the tangent ratio for ∠t.

a. 35/12
b. 35/37
c. 37/35
d. 12/35

Explanation:

Step1: Recall tangent - ratio formula

The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle T$ in right - triangle $RST$, the side opposite $\angle T$ is $RS = 35$ and the side adjacent to $\angle T$ is $ST$.
We can find $ST$ using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 37$ (hypotenuse) and $a = 35$ (one leg). Let $ST=x$, then $x^{2}+35^{2}=37^{2}$. So $x^{2}=37^{2}-35^{2}=(37 + 35)(37 - 35)=(72)\times(2)=144$, and $x = 12$.

Step2: Calculate the tangent ratio

$\tan T=\frac{\text{opposite}}{\text{adjacent}}=\frac{RS}{ST}$. Since $RS = 35$ and $ST = 12$, $\tan T=\frac{35}{12}$.

Answer:

A. $\frac{35}{12}$