Question

find hj.
triangle image with right angle at i, angle at j is 49°, side hi is 7
write your answer as an integer or as a decimal rounded to the nearest tenth.
hj =

Explanation:

Step1: Identify trigonometric ratio

We use the sine function: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$
Here, $\angle J = 49^\circ$, opposite side to $\angle J$ is $HI = 7$, hypotenuse is $HJ$ (the side we need to find).

Step2: Rearrange to solve for HJ

Rearrange the sine formula to isolate $HJ$:
$HJ = \frac{HI}{\sin(\angle J)}$

Step3: Substitute values and calculate

Substitute $HI=7$ and $\angle J=49^\circ$:
$HJ = \frac{7}{\sin(49^\circ)}$
Calculate $\sin(49^\circ) \approx 0.7547$, so:
$HJ \approx \frac{7}{0.7547} \approx 9.3$

Answer:

9.3