A 14-foot ladder makes a 62 degree angle with the ground. To the nearest foot, how far up the house does the ladder reach?
1 answer:
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Answer:
a = 21
b = 63
c = 42√3
d = 21√3
Step-by-step explanation:
The sides of a 30°-60°-90° triangle have the ratios 1 : √3 : 2. The given side (42) is the longest side of the smallest triangle, and the shortest side of the largest triangle.
That means the other sides of the smallest triangle will be ...
a = 42/2 = 21
a+b = 2(42) = 84
b = (a+b) -a = 84 -21 = 63
d = 21√3 . . . . middle-length side of the smallest triangle
c = 42√3 . . . . middle-length side of the largest triangle
The values of the variables are ...
- a = 21
- b = 63
- c = 42√3
- d = 21√3
The width and height of Talia's Scale drawing are :
- Width = 4.35 in
- Height = 5.7 in
We can obtain the actual length of the side of the house from Mike's drawing :
- Mike's scale = 3 ft to 1 in
Actual measurements:
- Scale ratio × model drawing
- Height, h = 9.5 × 3 = 28.5 feets
- Width, w = 7.25 × 3 = 21.75 feets
Measurement of Talia's Scale drawing :
- Talia's scale = 5 ft to 1 in
- Actual measurement ÷ scale
- Height = 28.5 ÷ 5 = 5.7 in
- Width = 21.75 ÷ 5 = 4.35 in
The width and height of Talia's scale drawing are 5.7 and 4.35 respectively.
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