Trigonometry Answers

A ladder that is 16 ft long is leaning against the side of a building. If the angle formed between the ladder and the ground is 72 degrees, how far is the bottom of the ladder from the base of the building?

A 70 lb bag of rice is being pulled by a person by applying a force F at an angle θ as shown. The force required to drag the bag is given by: F(θ)=70μ/μsinθ+cosθ where μ=0.35 is the friction coefficient. (a) Determine F(θ) for θ= 5°, 10°, 15°, 20°, 25°, 30°, 35° (b) Determine the angle θ where F is minimum. Do it by creating a vector θ with elements ranging from 5°to 35°and spacing of 0.01. CalculateF for each value of θ and then find the maximum F and associated θ with MATLAB's built-in function max

Given that the cosine of an angle is cos (∅) = 1/2°, what height of the triangle formed by this? ( The terminal point for this angle is (1,y) solve for y ).

Find the value of the cosecant of an angle given that the point on the terminal side of an angle is (3,4)

If the terminal side of ∅ is in the second quadrant and sin ∅ = 2/3. Find the values of the trigonometric functions of ∅.

If the terminal side of angle ∅ is in first quadrant and tan ∅ is 1/√3. Find the values of the other trigonometric functions of ∅.

Sketch the graph of the following function in one rectangular coordinate plane. Compare the behavior of each of the following graphs to the graph of y = sin x in terms of period, amplitude, and phase shift.

y=2sin x-4

y=sin 2x+3π2

y=sin 2x+2

Two buildings are 20 m apart. The angle from the top of the shorter building to

the top of the taller building is 20°. The angle from the top of the shorter building

to the base of the taller building is 45°. What is the height of the taller building?

Make sure to include a diagram and concluding sentence.

Elon Musk is watching his SpaceX shuttle launch. Calculate the angle of

elevation of the SpaceX shuttle, from his position located 8 km away, when the

shuttle reaches a height of 3500 m. Make sure to include a diagram and

concluding sentence.

Show that the points (-3,9), (3,5) and (1,2), are the vertices of a right triangle and find its area.