Math 10 Applied Trigonometry Questions

alyssa · #1 Jan 3, 2005, 04:22 PM

Argh trig. =[ The correct answers are beside the questions.

2. The longest slide in the world is in Vermont, U.S.A. It drops 213 m in a horizontal distance of 1200 m.

a) How long is the slide? 1219 m

b) What is its angle of inclination? 10degrees

3. The angle of elevation of the sun is 68degrees when a tree casts a shadow 14.3 m long. How tall is the tree? 35.4 m

4. A tightrope walker attaches a cable to the roofs of two adjacent buildings. The cable is 21.5 m long. The angle of inclination of the cable is 12degrees. The buildings are 21.0 m apart. The shorter building is 10.0 m high. What is the height of the taller building? 14.5 m

5. An architect plans to build a wheelchair ramp with a rise of 0.6 m. Safety standards indicate that the ramp may have an angle of inclination of 8degrees. How long must the ramp be? 4.3 m

6. An airplane is flying at an altitude of 6000 m over the ocean directly toward the coastline. At a certain time, the angle of depression to the coastline from the airplane is 14degrees. How much farther does the airplane have to fly before it reaches the coastline? 24km

A few important trig chapter questions:

1. [Reader's digest version]

c) Calculate the angle formed at A.

d) Calculate the bearing of A from B.

2. Jose wants to find the height of a radio tower situated on top of a building. Lying on the ground, 10 m from the base of the building, Jose finds the angle of elevation to the top of the building to be 83.2degrees, and the angle of elevation to the top of the tower to be 83.6degrees. What is the height of the radio tower, to the nearest tenth of a metre.

3. The Leaning Tower of Pisa was once vertical. However, the ground under the building is unstable and because of this, the tower now leans. The angle the tower makes with the ground is about 79.9degrees. At noon on June 21, 1997, the angle of elevation of the sun was 69.7degrees, and the length of the shadow of the tower was 14.8 m. What is the length of the tower on the side of the shadow, to the nearest tenth of a metre?

5. A golfer is standing 350 m from a hole on a golf course. The golfer's first drive of 210 m is 15degrees to the right of the direct line to the hole.

What is the remaing distance, d, to the hole, to the nearest metre?

Thanks in advance. =)

reinsuranc · Jan 26, 2005, 04:13 AM

I'll answer the first one:

Use the Pythagorean Theorem to calculate the hypotenuse of a right triangle whose height is 1200 and whose base is 213:

a^2 + b^2 = c^2
(1200)^2 + (213)^2 = c^2
c = 1219

The angle of inclination x can be calculated using any of sine, cosine or tangent. I'll use tangent: tan x = opposite/adjacent = 213/1200 = .18
Using a trig table the value of x corresponding to tan x = .18 is x = 10 degrees.

CroCivic91 · Jan 26, 2005, 01:04 PM

The idea with all of these problems is to draw what you have and what you need. For instance, let's see the "tree" problem.

html Code:

|\
| \ <- on the left side - tree - H
|  \
|   \
|____\ <- ANGLE
 shadow <- L

So you have the tree, and when sun is shining, it casts a shadow. The angle at which sun rays are coming down is given, so you know the lower left angle (in the picture) - let's call that angle "ANGLE". You also know how long the shadow is - let's call that length "L". So you can use any of the standard trigonometry formulas to calculate the height of the tree - let's call the height "H". For example: tan(ANGLE) = H / L. From this we get that H = L * tan( ANGLE ) and there's your solution.

Basically, just draw what you are given and use your standard formulas for every one of your problems.

Kresho



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