Question

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

diagram with vertical side 4.1, horizontal side 9.5
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.

diagram: right triangle mkn, right angle at m, mn=11, mk=5
a. 63.0° b. 24.4° c. 65.6° d.
the base of a ladder is 0.5 m from a wall of a house. the top of the ladder 5 m above the ground. determine the angle the ladder makes with the ho
termine the angle of inclination of the line to the nearest tenth of a deg
diagram: vertical dashed side 6.7, horizontal side 4.2, right angle

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, find \( \frac{4.1}{9.5} \approx 0.4316 \). Then, take the arctangent: \( \theta = \arctan(0.4316) \approx 23.3^\circ \)

Step1: Identify the trigonometric ratio

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

Step2: Calculate the angle

First, \( \frac{5}{11} \approx 0.4545 \). Then, \( \angle N = \arctan(0.4545) \approx 24.4^\circ \)

Step1: Identify the trigonometric ratio

We have a right triangle with opposite side \( 5 \) m (height) and adjacent side \( 0.5 \) m (base). The angle \( \theta \) between ladder and ground: \( \tan(\theta) = \frac{5}{0.5} = 10 \)

Step2: Calculate the angle

\( \theta = \arctan(10) \approx 84.3^\circ \) (Note: If the height was misread, but with given \( 0.5 \) and \( 5 \), this is the calculation. If height was different, adjust. But with given numbers, \( \tan(\theta)=\frac{5}{0.5}=10 \), \( \theta \approx 84.3^\circ \))

Answer:

b. \( 23.3^\circ \)

Question 5