The tallest television transmitting tower in the world is in North Dakota. From a point on level ground 5280 feet (one mile) fr
om the base of the tower, the angle of elevation is 29.4 degrees. Approximate the height of the tower to the nearest foot.
1 answer:
Answer:
2975 foot
Step-by-step explanation:
Let the tower be BC as shown in the diagram.
The distance from a point A on the level ground to the base B of the tower is 5280 feet.
We want to determine the height BC of the tower.
Using trigonometry
Tan θ =Opposite/Adjacent
Tan 29.4°=BC/5280
BC= 5280 X Tan 29.4°
=2975.12709969007
The height of the tower =2975 foot(to the nearest foot)
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9514 1404 393
Answer:
252.8 cm²
Step-by-step explanation:
The missing side of the right triangle can be found from the Pythagorean theorem:
s² = 20² -16² = 400 -256 = 144
s = 12 . . . . cm
The area of a right triangle is more easily found using the traditional area formula:
A = 1/2bh
A = 1/2(12 cm)(16 cm) = 96 cm² (left-side triangle)
The area of the triangle on the right can be found from Heron's formula. The semiperimeter is ...
s = (16 +20 +23)/2 = 29.5
The area is ...
A = √(29.5(29.5 -16)(29.5 -20)(29.5 -23)) = √(29.5·13.5·9.5·6.5)
A = √24591.9375 ≈ 156.818 . . . . . cm² (right-side triangle)
Then the total area of the figure is ...
A = 96 cm² +156.818 cm² = 252.818 cm² . . . . total area
