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Whitepunk [10]
3 years ago
13

The sun casts a 70 foot shadow on a 30 foot tree. Find the angle of elevation to the nearest degree.

Mathematics
1 answer:
Nesterboy [21]3 years ago
8 0

Answer:

23°

Step-by-step explanation:

We apply Pythagorean theorem to determine the missing length, Hypotenuse:

h^2+b^2=H^2\\\\70^2+30^2=H^2\\\\H=\sqrt{5800}\\\\=76.15773\ ft

This hypotenuse corresponds to the right triangle and the tree's height, corresponds to the angle of elevation:

-We apply the law of Sines;

\frac{a}{Sin \ A}=\frac{b}{Sin\ B}\\\\\\\frac{76.15773}{Sin \ 90}=\frac{30}{Sin\  h}\\\\h=Sin^{-1}\frac{30}{76.15773}\\\\=23.19859\approx 23\textdegree

Hence, the angle of elevation is 23°

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The average age of staff in the maths department is 40.
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Answer:

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The given parameters are;

The average age of the staffs in the mathematics department = 40

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The average age of Andy, Alan and Cathy = 43

From the given parameters, we have;

The average age of the staffs in the mathematics department = (The sum total of the ages of the members of the math department)/(The number of staffs in the department)

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From which we have;

The sum total of the ages of the members of the math department = 40 × 7 = 280

Which gives;

Jill's age + Nicky's age + Wendy's age + Cathy's age + Cerian's age + Alan's age + Andy's age = 280 years

The average age of Jill, Nicky and Wendy = 41

Given that Jill, Nicky, and Wendy make up 3 of the 7 members of staffs, we have;

The average age of Jill, Nicky and Wendy = (The sum total of the ages of Jill, Nicky, and Wendy)/(The number of staff Jill, Nicky, and Wendt make)

Therefore;

The sum total of the ages of Jill, Nicky, and Wendy = 41 × 3 = 123

Which gives;

Jill's age + Nicky's age + Wendy's age = 123 years

Similarly, the sum total of the ages of Andy, Alan, and Cathy = 43 × 3 = 129

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Andy's age + Alan's age + Cathy's age = 129 years

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∴ Cerian's age = 280 years - 123 years - 129 years = 28 years

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