9. You are standing on a mountain that is 6842 feet high. You are looking down at your campsite, creating an angle of depression
of 38°. If your eyes are 5.6 feet above the mountain how far is the base of the mountain from the campsite? (Round to the nearest hundredth)
1 answer:
Answer:
<u>8,764.53 feet</u>
Step-by-step explanation:
See the attached figure which represents the question.
Let the distance between campsite and the base of the mountain = d
The total height = 6842 + 5.6 = 6,847.6 feet.
As shown at the graph, the angle x and the depression angle are alternate angles, so they are congruent.
∴∠x = 38°
tan x = opposite/adjacent = (total height)/d = 6847.6/d
So, d = 6847.6/tan x
= 6847.6/tan 38° = 8,764.53 feet (to the nearest hundredth)
so, the distance between campsite and the base of the mountain = 8,764.53 feet
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Answer:
the largest angle of the field is 149⁰
Step-by-step explanation:
Given;
perimeter of the triangular filed, P = 120 m
length of two known sides, a and b = 21 m and 40 m respectively
The length of the third side is calculated as follows;
a + b + c = P
21 m + 40 m + c = 120 m
61 m + c = 120 m
c = 120 m - 61 m
c = 59 m
B
↓ ↓
↓ ↓
↓ ↓
A → → → → → → → → → → → C
Consider ABC as the triangular field;
Angle A is calculated by applying cosine rule;
Angle B is calculated as follows;
Angle C is calculated as follows;
Therefore, the largest angle of the field is 149⁰.