Question

A)
Dedrea is making a bike ramp on the sidewalk in front of their house. They place a wood plank ontop of blocks to form the ramp. The blocks are one foot in height, and the distance from the base of theblocks to where the wood plank touches the sidewalk is five feet. What is the approximate angle formedbetween the sidewalk and the base of the ramp?
(1 point)
11°
45°
79°
23°
A)
Right triangle
is drawn on paper. The right angle is located at vertex
with side length
as the hypotenuse. The side length measurements are
,
, and
. What is the approximate angle measure at vertex
?
(1 point)
LMN L
MN LM = 8 units MN = 10 units
NL = 6 units N
37°
31°
53°
39°

Answer 1

1) 11°.
Reason: slope angle θ satisfies tan θ = rise/run = 1/5 ⇒ θ = arctan(0.2) ≈ 11.3°.

2) 53°.
Reason: MN = 10 is the hypotenuse, LM = 8 is opposite angle N, so sin N = 8/10 = 0.8 ⇒ N ≈ arcsin(0.8) ≈ 53.1°.