Question

solve the right triangle.
write your answers as integers or as decimals rounded to the nearest tenth.
jk =
ik =
m∠j = °
submit

Explanation:

Step1: Find $\angle J$

Sum of angles in triangle is $180^\circ$.
$m\angle J = 180^\circ - 90^\circ - 56^\circ = 34^\circ$

Step2: Calculate $IK$ (adjacent to $\angle I$)

Use cosine of $\angle I$: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$IK = \sqrt{89} \times \cos(56^\circ) \approx 9.434 \times 0.5592 \approx 5.3$

Step3: Calculate $JK$ (opposite to $\angle I$)

Use sine of $\angle I$: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$JK = \sqrt{89} \times \sin(56^\circ) \approx 9.434 \times 0.8290 \approx 7.8$

Answer:

$JK = 7.8$
$IK = 5.3$
$m\angle J = 34^\circ$