Viola drives 2 kilometers up a hill that makes an angle of 9 with the horizontal. To the nearest tenth of a kilometer, what horizontal distance has she covered? Group of answer choices 12.6 km 3.2 km 2 km 0.3 km

Choice 2 km is right

Step-by-step explanation:

Let x be the horizontal distance covered by Viola.

Given:

Viola drives up-side of a hill = 2 km

Make an angle with horizontal (Theta = 9°)

We need to find the horizontal distance covered by Viola.

Solution:

First we draw a triangle abc where ab = 2 km, ac = x and ∠cab = 9°.

Using cosine law.

from the figure adjacent = ac and hypotenuse = ab.

Substitute ab = 2, ac = x and (Theta = 9°).

x ≅ 2 km

Therefore, horizontal distance covered by Viola is approx 2 km.

part a: triangles gcb and epb

part b. sides cg and rp are parallel by definition of parallelogram.

angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.

part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.

calculation of be:

gb/be = cb/bp

(400 ft)/be = 300/200

(400 ft)/be = 3/2

3be = 2 * 400 ft

3be = 800 ft

be = 800/3 ft

calculation of pe:

gc/pe = cb/bp

(350 ft)/pe = 300/200

(350 ft)/pe = 3/2

3pe = 2 * 350 ft

3pe = 700 ft

pe = 700/3 ft