Question

1. consider this triangle.

write an expression that can be used to find the length of side jh and an expression that can be used to find the length of side gj

Explanation:

Step1: Identify triangle properties

This is a right triangle ($\angle I = 90^\circ$), $\angle G = 35^\circ$, hypotenuse $GH = 9$.

Step2: Solve for $JH$ (opposite $\angle G$)

Use sine function: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(35^\circ) = \frac{JH}{9}$
Rearrange to isolate $JH$:
$JH = 9\sin(35^\circ)$

Step3: Solve for $GJ$ (adjacent to $\angle G$)

Use cosine function: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(35^\circ) = \frac{GJ}{9}$
Rearrange to isolate $GJ$:
$GJ = 9\cos(35^\circ)$

Answer:

Length of $JH$: $\boldsymbol{9\sin(35^\circ)}$
Length of $GJ$: $\boldsymbol{9\cos(35^\circ)}$