Question

use the figure below to answer the following questions. round all answers to two decimal places. enter deg after any degree values.
enter deg after any degree value.
a) what is ( mangle k )?
not quite.
b) what is ( jl )?
not quite.
c) what is ( kl )?
thats not it

Explanation:

Step1: Find \( m\angle K \)

In a right triangle, the sum of angles is \( 180^\circ \). Given \( \angle L = 90^\circ \) and \( \angle J = 65^\circ \), so \( m\angle K = 180^\circ - 90^\circ - 65^\circ = 25^\circ \).

Step2: Find \( JL \)

Using cosine in \( \triangle JLK \), \( \cos(65^\circ) = \frac{JL}{JK} \). \( JK = 19 \), so \( JL = 19 \times \cos(65^\circ) \approx 19 \times 0.4226 \approx 8.03 \).

Step3: Find \( KL \)

Using sine in \( \triangle JLK \), \( \sin(65^\circ) = \frac{KL}{JK} \). \( JK = 19 \), so \( KL = 19 \times \sin(65^\circ) \approx 19 \times 0.9063 \approx 17.22 \).

Answer:

a) \( 25.00 \) deg
b) \( 8.03 \)
c) \( 17.22 \)