Question

lesson 6: working with trigonometric ratios
cool down: more unknown triangle measures
find all the unknown side and angle measures in this triangle.
24°
8

Explanation:

Step1: Find angle at L

The sum of angles in a triangle is $180^\circ$. For right triangle $MKL$, $\angle L = 180^\circ - 90^\circ - 24^\circ$
$\angle L = 66^\circ$

Step2: Calculate side KL (opposite $\angle M$)

Use tangent ratio: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(24^\circ)=\frac{KL}{8}$
$KL = 8\times\tan(24^\circ) \approx 8\times0.4452 = 3.56$

Step3: Calculate side ML (hypotenuse)

Use cosine ratio: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(24^\circ)=\frac{8}{ML}$
$ML = \frac{8}{\cos(24^\circ)} \approx \frac{8}{0.9135} = 8.76$

Answer:

• $\angle L = 66^\circ$
• Length of $KL \approx 3.56$
• Length of $ML \approx 8.76$