We need to solve problems 15, 16, 17 and 18 from the image. Problem 15: Find the value of $\sin L$ rounded to the nearest hundredth, if necessary, for the given triangle. Problem 16: Find the value of $\cos R$ rounded to the nearest hundredth, if necessary, for the given triangle. Problem 17: Solve for $x$. Round to the nearest tenth, if necessary. Problem 18: Solve for $x$. Round to the nearest tenth, if necessary.

1. Problem Description

We need to solve problems 15, 16, 17 and 18 from the image.

Problem 15: Find the value of $\sin L$ rounded to the nearest hundredth, if necessary, for the given triangle.

Problem 16: Find the value of $\cos R$ rounded to the nearest hundredth, if necessary, for the given triangle.

Problem 17: Solve for $x$. Round to the nearest tenth, if necessary.

Problem 18: Solve for $x$. Round to the nearest tenth, if necessary.

2. Solution Steps

Problem 15:

In a right triangle, $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$.

In the given triangle, the side opposite to angle $L$ is 2, and the hypotenuse is

7. Therefore, $\sin L = \frac{2}{7}$.

$\sin L \approx 0.2857$

Rounding to the nearest hundredth, $\sin L \approx 0.29$.

Problem 16:

In a right triangle, $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$.

In the given triangle, the side adjacent to angle $R$ is 14, and the hypotenuse is

2

9. Therefore, $\cos R = \frac{14}{29}$.

$\cos R \approx 0.4827$

Rounding to the nearest hundredth, $\cos R \approx 0.48$.

Problem 17:

We are given a triangle $LMN$ with $LM = x$, $MN = 45$, and angle $LNM = 64^\circ$. Angle $LMN = 90^\circ$.

Using the sine function:

$\sin(64^\circ) = \frac{x}{45}$

$x = 45 \sin(64^\circ)$

$x \approx 45 \times 0.8988$

$x \approx 40.446$

Rounding to the nearest tenth, $x \approx 40.4$.

Problem 18:

We are given a triangle $KLM$ with $LM = 72$, angle $KML = 22^\circ$, and angle $KLM = 90^\circ$. $KM = x$.

Using the cosine function:

$\cos(22^\circ) = \frac{x}{72}$

$x = 72 \cos(22^\circ)$

$x \approx 72 \times 0.9272$

$x \approx 66.758$

Rounding to the nearest tenth, $x \approx 66.8$.

3. Final Answer

Problem 15: $\sin L \approx 0.29$

Problem 16: $\cos R \approx 0.48$

Problem 17: $x \approx 40.4$

Problem 18: $x \approx 66.8$