From a horizontal distance of 8.5 km, a pilot observes that the angles of depression of the top and base of a control tower are 30° and 33°, respectively. Calculate correct to three significant figures, the: (a) shortest distance between the pilot and the base of the control tower (b) height of the control tower. (WAEC)
From a horizontal distance of 8.5 km, a pilot observes that the angles of depression of the top and base of a control tower are 30° and 33°, respectively. Calculate correct to three significant figures, the: (a) shortest distance between the pilot and the base of the control tower (b) height of the control tower. (WAEC)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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No 9
Transcribed Image Text:the sun, correct to the nearest de
flag pole was 44°. If the foot of the pole is
25 m from the foot of the building and on
the same horizontal ground, find, correct
that the angle of depression of the top of
7 A woman looking out from the window of
6 A boy looks through a window of a build
away from the foot of the building. It w
If the shadow of a pole 7 m high is
depression of the mango from the window.
window is 9 m from the ground, caleculate
correct to the nearest degree, tha angle of
and sees a mango fruit on the ground SO
190
Essential mathematics for senior secondary schools (2)
its length, what is the angle of
y another
If the
150 m
(WAEC)
In A WQS using Pythagoras theorem:
WS = WQ? + QS²
Substituting (i) and (ii) in (iii)
e distance
the d
A vertical Do
A student r
the a
is
1502=
tan 40°
tan 35°
observes th
150 =
tan 40°
(WASSCE)
a building at a height of 30 m
top of the
angle of
35° Wh
moves 10
tan 35°
1
22 500=h?
observed
1
(0.83912
0.70022
1
22 500=h²
(0.7041
22 500 = h²(1.420 + 2.040)
0.4903
13.6 Bes
to the nearest whole number, the
(a) angle of depression of the foot of
paints and
in the ai
bearings
22 500 = 3.46h2
A bearing i
h2=
22 500
pole from the woman
(b) height of the flag pole. (WASSCE)
8 From the top of a building, Deborah ob
serves that the angles of depression of tye
vehicles to be 35° and 47°. The two ve
hicles are on the same straight line with the
building and also on the same side of the
building. Calculate to the nearest metre the
height of the building if the distance
between the vehicles is 10 m.
9 From a horizontal distance of 8.5 km, a pilot
6503 cm
3.46
h= 6503 m =80.64 m
h = 80.6 m to 3 s.f.
In comp
from N
Exercise 13.6
pearer
For ex
IA woman 1.65 m tall stood 50 m away from
the foot of a tower and observed that the
angle of elevation of the top of the tower
to be 50°. What is the height of the tower?
A young man 1.7 m tall, while standing,
measures the angle of elevation of the top
of a pole as 40°. If he is 15 m from the
pole, what is the height of the pole?
3 The angle of depression of a boat from the
midpoint of a vertical cliff is 35°. If the
boat is 120 m from the foot of the cliff,
calculate the height of the cliff. (WASSCE)
4The angle of elevation of a tower, 45 m high
observes that the angles of depression of
the top and base of a control tower are 30°
and 33°, respectively. Calculate correct to
three significant figures, the:
(a) shortest distance between the pilot and
the base of the control tower
(b) height of the control tower. (WAEC)
10 (a) The triangle ABC has sides
AB = 17 m, BC = 12 m and AC = 10 m.
from a ball on the ground is 52°.
(a) How far is the ball from the foot of the
Calculate:
tower?
(b) How much further away should the ball
(i) the largest angle of the triangle
(ii) the area of the triangle.
(b) From a point T on a horizontal ground.
be moved from the foot of the tower,
so that the angle of elevation is halved?
the angle of elevation of the top R of
tower RS, 38 m high is 63°. Cal
correct to the nearest metr
distance between T an (WA
From a po
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