Question

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29. A tree casts a shadow that is 12 feet long. If the tree is 20 feet tall, what is the angle of elevation of the sun? Draw a diagram to represent the situation. Round the answer to the nearest tenth.


30. In ΔABC, m∠A = 75°, m∠B = 50°, and c = 9. Draw ΔABC, then use the Law of Sines to find a. Round final answer to the nearest tenth.

Answer 1

• Question 29: Angle of Elevation is -------> 59.0°

• Question 30: The length of side A in --------> △ABC is approximately 10.3

• Explanation:

• Question 29: In this question, we can use the tangent function to solve the problem. We can set the Sun's elevation angle as theta (θ). Then we can get the equation:

tan (θ) = 20/12, and solve for θ

• Solve the problem:

• We can draw a right triangle with the tree, the shadow, and the Sun.

• The tree's height is the opposite side, and the length of the shadow is the adjacent side.
• The angle of the sun's elevation is the angle between the ground and the line from the top of the tree to the sun.

• We can set the angle of elevation of the sun as theta (θ).

We then get the equation tan (θ) = 20/12

• We can solve for theta (θ) using the equation

θ = arctan(5/3)

• We can use a calculator to find that:

• Let the angle of elevation = θ

Tan θ = opp/adj

Tan θ = 20/12

θ = Tan^-1 (20/12)

θ = 59.03624346 degrees

θ = 59.0 degrees

• Draw the conclusion:

Hence, the Angle of Elevation is -------> 59.0°

• Question 30: △

m < C = 180 degrees - m<A - m<B

m<C = 180 degrees - 75 degrees - 50 degrees

• Simplify:

m<C = 55 degrees

• Apply the Law of Sines:

a/sin A = c/sin C

• Substitute the values:

a/sin 75 degrees = 9/sin 55 degrees

• Solve for A:

a = 9 * sin 75 degrees/sin 55 degrees

• Calculate the value of A:

a = 10.3

• Draw a conclusion:

Therefore, The length of side A in --------> △ABC is approximately 10.3

Hope this helps you!

Answer 2

29. 59.06°

30. 10.6

Explanation:

29.
By using the Tangent angle rule, we can find the angle of elevation,

We know that

Tan Angle = opposite/adjacent

Tan x=AB/BC

Tan x=20/12

Tan x=5/3

`x=Tan^(- )((5)/(3))`

x=59.06°

30.

The law of sine is a formula that can be used to find the lengths of the sides of a triangle, or to find the angles of a triangle, when two sides and the angle between them are known. The formula is:

a / sin(A) = b / sin(B) = c / sin(C)

Here taking

a / sin(A) = c / sin(C)

here A=75°, C=180-75-50=55° and c -9 and

we need to find a,

substituting value

a/Sin(75°)=9/Sin(55°)

a=9*Sin(75°)/Sin(55°)

a=10.61

Therefore, the value of a is 10.6