Question

name: ______________

1. determine the angle of inclination of the line to the nearest tenth of a degree.

image of right triangle: vertical dashed line 4.1, horizontal 9.5, right angle at bottom left
a. 64.4° b. 23.3° c. 66.7° d. 25.6°

1. determine the measure of ∠n to the nearest tenth of a degree.

image of right triangle: right angle at m, mn=11, mk=5
a. 63.0° b. 24.4° c. 65.6° d. 27.0°
short answer

1. the base of a ladder is 0.5 m from a wall of a house. the top of the ladder rests against the house 2.5 m above the ground. determine the angle the ladder makes with the house, to the nearest degree.
2. determine the angle of inclination of the line to the nearest tenth of a degree.

image of right triangle: vertical dashed line 6.7, horizontal 4.2, right angle at bottom right

Explanation:

Question 4

Step1: Identify the trigonometric ratio

We have a right triangle with opposite side \( 4.1 \) and adjacent side \( 9.5 \). The angle of inclination \( \theta \) can be found using the tangent function: \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{4.1}{9.5} \)

Step2: Calculate the angle

First, calculate \( \frac{4.1}{9.5}\approx0.4316 \). Then, take the arctangent: \( \theta = \arctan(0.4316) \)
Using a calculator, \( \theta\approx23.3^\circ \)

Step1: Identify the trigonometric ratio

In right triangle \( \triangle KMN \), \( \angle M = 90^\circ \), \( KM = 5 \), \( MN = 11 \). For \( \angle N \), the opposite side is \( KM = 5 \) and adjacent side is \( MN = 11 \). So \( \tan\angle N=\frac{KM}{MN}=\frac{5}{11} \)

Step2: Calculate the angle

First, calculate \( \frac{5}{11}\approx0.4545 \). Then, take the arctangent: \( \angle N=\arctan(0.4545) \)
Using a calculator, \( \angle N\approx24.4^\circ \)

Step1: Identify the triangle sides

The base of the ladder (distance from wall) is \( 0.5 \) m (opposite side to the angle with the house), and the height on the house is \( 2.5 \) m (adjacent side to the angle with the house). Let the angle be \( \theta \), then \( \tan\theta=\frac{0.5}{2.5}=0.2 \)

Step2: Calculate the angle

Take the arctangent: \( \theta=\arctan(0.2) \)
Using a calculator, \( \theta\approx11.3^\circ\approx11^\circ \) (to the nearest degree)

Answer:

b. \( 23.3^\circ \)

Question 5