A hot-air balloon is tied to the ground with two taut ropes. One rope is directly under the balloon and makes a right angle with
the ground. The other rope forms an angle of 60º with the ground. Which statements are correct?
A) d ≈ 60 ft.
B) d ≈ 66 ft.
C) h ≈ 104 ft.
D) h ≈ 108 ft.
E) angle of depression = 30°
A) d ≈ 60 ft.
B) d ≈ 66 ft.
C) h ≈ 104 ft.
D) h ≈ 108 ft.
E) angle of depression = 30°
1 answer:
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Answer:
Step-by-step explanation:
I'm going to use instead of
because it is less characters for me to type.
I'm going to start with the left hand side and see if I can turn it into the right hand side.
I'm going to use a cofunction identity for the 2nd term.
This is the identity: I'm going to use there.
I'm going to rewrite this in terms of and
because I prefer to work in those terms. My objective here is to some how write this sum as a product.
I'm going to first use these quotient identities: and
So we have:
I'm going to factor out because if I do that I will have the
factor I see on the right by the reciprocal identity:
Now I need to somehow show right right factor of this is equal to the right factor of the right hand side.
That is, I need to show is equal to
.
So since I want one term I'm going to write as a single fraction first:
Find a common denominator which is :
By the Pythagorean Identity I can rewrite the top as 1:
By the quotient identity , I can rewrite this as:
By the cofunction identity , we have the second factor of the right hand side:
Let's just do it all together without all the words now: