Trigonometry Answers

Two planes leave the Ottawa airport at the same time travelling at 920 km/h and 780 km/h. how far apart are the two planes after 3 hours, if the angle between their flight paths is 26°?

The terminal arm of an angle is standard position passes through 𝑃(−5,5).

a. Sketch a diagram of an angle in standard position.

b. Determine the length of the hypotenuse.

c. Determine the primary trigonometric ratios to three decimal places.

Solve for angleT△𝑅𝑆𝑇, given 𝑟=1.2𝑘𝑚, 𝑠=2.4𝑘𝑚, 𝑡=2.2𝑘𝑚

Include a diagram for each question.

Solve for sidef in△𝐷𝐸𝐹,given 𝑒=2.1𝑖𝑛, ∠𝑓=72°, ∠𝑑=60°.

Include a diagram for each question.

Solve triangle △ 𝑋𝑌𝑍, given ∠𝑋 = 90°, 𝑥 = 21𝑐𝑚, 𝑧 = 15𝑐𝑚

The entrance to a health clinic is x feet above street level. A ramp is installed from street level to the entrance of the health clinic which has an angle of inclination of 5 ◦ . The ramp is 10 feet long. What is x?

Solve for x in degrees, where 0 degrees <= x < 360 degrees . 2sin^2 x - sin x = 1

A weight on the end of a spring oscillating in harmonic motion. The equation model for oscillation is d (t) = 6 sin, where d is the distance (in centimeter) from the equilibrium point in t sec.

a.  What is the period of the motion? What is the frequency of the motion? 

b.  What is the placement from the equilibrium at t = 2.5? Is the weight moving toward the equilibrium at this time?

c.  What is the displacement from equilibrium at t = 3.5? Is the weight moving toward the equilibrium point or away from the equilibrium at this time?

d.  How far does the weight move between t = 1 and t = 1.5 sec?

e. What is the average velocity for this interval? 

y=5+8cos[pi(x-1)]

y=2+3cos2x

draw 2 periods

or 2 cycles

the radial displacement of the top a tower respect to its base on a single aerial photo is 4.1 mm and the top of the tower is 73.8 mm from the nadir. if the tower is 500 feet tall and the base of the tower is 1000 feet above sea level, what was the flying height of the aircraft above sea level at the instant of exposure?