Homework PracticeSign Up
Back to assignmentPrintable assignment view
Print options

Homework Practice

Printable assignment

Heights and Distances Practice 1: Angles and Diagrams

Section A: Core Ideas

Question 1mcq
A student looking up from the ground to the top of a tower forms which angle with the horizontal line through the eye?
A.Angle of depression
B.Right angle only
C.Angle at the top of the tower
D.Angle of elevation
Question 2mcq
From the top of a lighthouse, an observer looks down at a boat. The angle made with the horizontal through the observer is called:
A.Central angle
B.Angle of rotation
C.Angle of depression
D.Angle of elevation
Question 3mcq
A 20 m tree casts a shadow, and the angle of elevation of the sun is 45∘45^\circ. Which diagram model is most appropriate?
A.A triangle with the shadow as hypotenuse
B.A right triangle with tree as vertical height and shadow as horizontal base
C.A circle with the tree as radius
D.Two unrelated right triangles
Question 4mcq
A tower height is unknown, the horizontal distance from its foot is known, and the angle of elevation is given. Which ratio is usually most direct?
A.tan⁡θ=heightdistance\tan\theta=\frac{\text{height}}{\text{distance}}
B.sin⁡θ=distanceheight\sin\theta=\frac{\text{distance}}{\text{height}}
C.cos⁡θ=heightdistance\cos\theta=\frac{\text{height}}{\text{distance}}
D.sec⁡θ=heighthypotenuse\sec\theta=\frac{\text{height}}{\text{hypotenuse}}
Question 5mcq
A man stands 30 m from a tower. The angle of elevation of the top is 30∘30^\circ. What is the tower height?
A.30330\sqrt{3} m
B.1515 m
C.6060 m
D.10310\sqrt{3} m

Section B: Apply and Check

Question 6mcq
A building is 24 m high. The angle of elevation of its top from a point on the ground is 45∘45^\circ. What is the distance from the building?
A.24224\sqrt2 m
B.4848 m
C.2424 m
D.1212 m
Question 7mcq
From two points on the same straight line with a tower, angles of elevation are 30∘30^\circ and 60∘60^\circ. What is the key modelling idea?
A.Use only the larger angle as the answer
B.Use two right triangles sharing the same vertical height
C.Use two separate heights
D.Ignore the nearer observation
Question 8mcq
Two observation points are on the same side of a tower, and the nearer point is 20 m from the farther point. Which base lengths are related correctly?
A.Farther distance = nearer distance + 20
B.Nearer distance = farther distance + 20
C.Both distances are equal
D.The 20 m is the tower height
Question 9mcq
Two observers stand on opposite sides of a tower. What does the distance between observers equal?
A.Difference of their distances
B.Height of the tower
C.Hypotenuse of one triangle
D.Sum of their distances from the foot of the tower
Question 10mcq
Which standard value is useful for a height problem with angle 60∘60^\circ and base 1010 m?
A.sin⁡60∘=12\sin60^\circ=\frac12
B.cos⁡60∘=3\cos60^\circ=\sqrt3
C.tan⁡60∘=3\tan60^\circ=\sqrt3
D.tan⁡60∘=1\tan60^\circ=1