**1. The angle of elevation of the top of a building from a point on the ground is 45o. If the distance from the point to the building is 50 metres, what is the height of the building?**

a) 25 metres

b) 50 metres

c) 75 metres

d) 100 metres

**Answer:** b) 50 metres

**Explanation:**

Given: Angle of elevation = 45^{o}, Distance from point to building = 50 metres

Let the height of the building be h metres.

We can use the tangent function to find the height of the building as follows:

tan (45^{o}) = h/50

Simplifying the equation, we get:

h = 50 x tan (45^{o})

Using the value of tan (45^{o}) = 1, we get:

h = 50 x 1

Therefore, the height of the building is 50 metres.

**2. A 10 metres tall tree is located 20 metres away from a building. The angle of elevation from the top of the tree to the top of the building is 30 ^{o}. What is the height of the building?**

a) 21.50 m

b) 32.64 m

c) 41.86 m

d) 53.45 m

**Answer:** a) 21.50 m

**Explanation:** Given: Height of the tree = 10 metres,

Distance from tree to building = 20 metres,

Angle of elevation = 30^{o}

Let the height of the building be h metres.

We can use the tangent function to find the height of the building as follows:

tan (30^{o}) = (h - 10) / 20

Simplifying the equation, we get:

h - 10 = 20 x tan (30^{o})

Using the value of tan (30^{o}) = 1/√3, we get

h - 10 = 20 x (1/√3)

h - 10 = (20/√3)

h = (20/√3) + 10

Simplifying further, we get:

h = (20 + 10√3) / √3

use √3 = 1.74

then, h = (20 + 10 x 1.74) / 1.74

Therefore, the height of the building is approximately 21.50 metres.

**3. The angle of depression of a boat from the top of a lighthouse is 60 ^{o}. If the height of the lighthouse is 50 metres, what is the distance between the boat and the lighthouse?**

a) 9.67metres

b) 11.25 metres

c) 28.87 metres

d) 31.05 metres

**Answer:** c) 28.87 metres

**Explanation:** Given: Angle of depression = 60^{o}, Height of the lighthouse = 50 metres.

Let the distance between the boat and the base of the lighthouse be d metres.

We can use the tangent function to find the distance between the boat and the lighthouse as follows:

tan (60^{o}) = 50 / d

Simplifying the equation, we get:

d = 50/tan (60^{o})

Using the value of tan (60^{o}) = √3, we get:

d = 50/√3

use √3 = 1.74

then, d = 50/1.74

d = 28.74 metres

Therefore, the distance between the boat and the base of the lighthouse is approximately 28.74 metres.

**4. A kite is flying at a height of 60 metres from the ground. The angle of elevation from a point on the ground to the kite is 45 ^{o}. What is the distance between the point and the kite**?

a) 60 metres

b) 80 metres

c) 100 metres

d) 120 metres

**Answer:** a) 60 metres

**Explanation:**

Given: Height of the kite = 60 metres, Angle of elevation = 45^{o}

Let the distance between the point on the ground and the kite be d metres.

We can use the tangent function to find the distance between the point and the kite as follows:

tan (45^{o}) = 60 / d

Simplifying the equation, we get:

d = 60 / tan (45^{o})

Using the value of tan (45^{o}) = 1, we get:

d = 60 / 1

Therefore, the distance between the point on the ground and the kite is 60 metres.

**5. The angles of elevation of top and bottom of a flag at a distance of 30 m are 45° and 30° respectively. What is the height of the flag AB?**

a) 10.54 metres

b) 10 metres

c) 20 metres

d) 12.68 metres

**Answers:** d) 12.68 m

**Explanations:**

tan 45° = AC/DC

AC = DC tan 45o

= 30 tan 45°

= 30 m

tan 30° = BC/DC

BC = DC tan 30°

BC = 30 tan 30°

= 30 x 1/√3

= 10√3 m

Height of flag AB = 30 - 10√3

= 30 - 17.32

= 12.68 m

**1. A 15-meter flagpole casts a 15-meter shadow. What is the angle of elevation of the sun?**

a) 30^{o}

b) 45^{o}

c) 60^{o}

d) 75^{o}

**Answers:** b) 45^{o}

**2. A building is 60 metres tall. From a certain point, the angle of elevation to the top of the building is 30 ^{o}. How far is the point from the building?**

a) 60√3 metres

b) 45√3 metres

c) 30√3 metres

d) 40√3 metres

**Answers:** a) 60√3 metres

**3. A ladder leans against a wall and makes an angle of 60 ^{o} with the ground. If the ladder is 10 metres long, how high up the wall does it reach?**

a) 10 metres

b) 9.61 metres

c) 8.7 metres

d) 11.5 metres

**Answers:** c) 8.7 metres

**4. The angle of depression from the top of a 15-metre-tall building to the bottom of a nearby tree is 30 ^{o}. What is the distance between the building and the tree?**

a) 35 metres

b) 25√3 metres

c) 15 metres

d) 15√3 metres

**Answers:** d) 15√3 metres

**5. The angle of elevation from a point 100 metres away from a tower to the top of the tower is 30 ^{o}. What is the height of the tower?**

a) 50 metres

b) 57.6 metres

c) 86.6 metres

d) 100 metres

**Answers:** b) 57.6 metres

**6. A tree casts a shadow 12 metres long. At the same time, a 5-metre tall pole nearby casts a shadow 3 metres long. What is the height of the tree?**

a) 15 metres

b) 20 metres

c) 25 metres

d) 30 metres

**Answers:** b) 20 metres

**7. A flagpole 21/√3 metres tall casts a shadow 7 metres long. What is the angle of elevation of the sun?**

a) 30^{o}

b) 45^{o}

c) 60^{o}

d) 75^{o}

**Answers:** c) 60^{o}

**8. The angle of elevation of a balloon from a point on the ground is 30 ^{o}. If the balloon is 150 metres above the ground, how far is it from the point on the ground?**

a) 154.4 metres

b) 259.5 metres

c) 352.3 metres

d) 473.2 metres

**Answers:** b) 259.5 metres

**9. A plane is flying at an altitude of 10,000 metres. If the angle of elevation to the plane from a point on the ground is 30 ^{o}, how far away is the plane from the point on the ground?**

a) 5,000 metres

b) 10,000 metres

c) 11,547 metres

d) 20,000 metres

**Answers:** d) 20,000 metres

**10. A cliff is 100 meters high. The angle of depression of a boat in the water at the base of the cliff is 45 ^{o}. What is the distance between the boat and the top of the cliff?**

a) 70.7 meters

b) 100 meters

c) 141.4 meters

d) 200 meters

**Answers:** c) 141.4 metres

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