Question

find hj.
write your answer as an integer or as a decimal rounded to the nearest tenth.
hj =
(the image shows a right triangle with right angle at h, angle at j is 56 degrees, and hypotenuse ij is 6.)

Explanation:

Step1: Identify adjacent side, hypotenuse

In right $\triangle HIJ$, $\angle J=56^\circ$, hypotenuse $IJ=6$, $HJ$ is adjacent to $\angle J$.

Step2: Use cosine ratio formula

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos(56^\circ)=\frac{HJ}{6}$

Step3: Solve for HJ

Rearrange to isolate $HJ$: $HJ=6\times\cos(56^\circ)$
Calculate $\cos(56^\circ)\approx0.5592$, so $HJ\approx6\times0.5592=3.3552$

Step4: Round to nearest tenth

Round $3.3552$ to 1 decimal place: $3.4$

Answer:

$3.4$