A boat is 60m from the base of a lighthouse. The angle of depression between the lighthouse and the boat is 37°. How tall is the
lighthouse.
1 answer:
Answer: 34.64 m
Step-by-step explanation:
Given: A boat is 60 m from the base of a lighthouse.
The angle of depression between the lighthouse and the boat is 37°.
By using trigonometric ratios :
here x= 37°, side opposite to x = height of lighthouse (h) , side adjacent to x = 60 m
Hence, the lighthouse is 34.64 m tall.
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Answer:
a) -13.9 ft/s
b) 13.9 ft/s
Step-by-step explanation:
a) The rate of his distance from the second base when he is halfway to first base can be found by differentiating the following Pythagorean theorem equation respect t:
(1)
(2)
Since:
When x = 45 (the batter is halfway to first base), D is:
Now, by introducing D = 100.62, x = 45 and dx/dt = 31 into equation (2) we have:
Hence, the rate of his distance from second base decreasing when he is halfway to first base is -13.9 ft/s.
b) The rate of his distance from third base increasing at the same moment is given by differentiating the folowing Pythagorean theorem equation respect t:
(3)
We have that D is:
By entering x = 45, dx/dt = 31 and D = 100.63 into equation (3) we have:
Therefore, the rate of the batter when he is from third base increasing at the same moment is 13.9 ft/s.
I hope it helps you!