Question

2 - 88. based on the measurements provided for each triangle below, determine whether the measure of x must be more than, less than, or equal to 45°. homework help
a.
3
4
b.
18
18

Explanation:

Step1: Recall tangent formula for right - triangle

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For part a, $\tan x=\frac{3}{4}$.

Step2: Compare with $\tan45^{\circ}$

We know that $\tan45^{\circ} = 1$. Since $\frac{3}{4}<1$, and the tangent function is increasing for $0^{\circ}<\theta<90^{\circ}$, then $x < 45^{\circ}$.

Step3: Analyze part b

In a right - triangle, if the two legs are equal (both 18 in this case), then $\tan x=\frac{18}{18}=1$.

Step4: Determine angle value

Since $\tan x = 1$ and for $0^{\circ}

Answer:

a. $x$ is less than $45^{\circ}$
b. $x$ is equal to $45^{\circ}$