Study of Measurement Using Clinometers - JSS3 Mathematics Past Questions and Answers - page 1
How can a clinometer be used to estimate the height of a tree?
Measure the angle of depression from the tree's base.
Measure the angle of depression from the tree's base.
Count the number of branches on the tree
Measure the circumference of the tree trunk
What is the primary function of a clinometer in navigation?
Measure the temperature of the ocean.
Determine the angle of elevation of the North Star.
Estimate the distance to an approaching ship
Measure the angle of celestial bodies above the horizon
In surveying, why is it important to measure angles accurately with a clinometer?
To estimate the weight of building materials.
To calculate the area of land accurately.
To determine the wind speed at construction sites.
To measure the depth of rivers
Scenario: Sarah wants to estimate the height of a flagpole in her school yard. She stands 30 meters away from the base of the flagpole and measures the angle of elevation to the top of the pole as 50 degrees. Calculate the height of the flagpole.
Given:
Distance from the flagpole (d) = 30 meters
Angle of elevation (θ) = 50 degrees
To find the height of the flagpole (h), use the formula:
ℎ=𝑑×tan(𝜃)
Substitute the given values:
ℎ=30×tan(50∘)
Calculate the height using a calculator:
ℎ≈30×1.192
ℎ≈35.76 meters
Scenario: John is on a hill and wants to measure the distance to a tall building in the city. He measures the angle of elevation to the top of the building as 30 degrees. If the building is known to be 50 meters tall, how far is John from the building?
Given:
Height of the building (h) = 50 meters
Angle of elevation (θ) = 30 degrees
To find the distance to the building (d), use the formula:
𝑑=ℎtan(𝜃)
Substitute the given values:
𝑑=50tan(30∘)
Calculate the distance using a calculator:
𝑑=50/0.577
𝑑≈86.6 meters
Scenario: John is on a hill and wants to measure the distance to a tall building in the city. He measures the angle of elevation to the top of the building as 30 degrees. If the building is known to be 50 meters tall, how far is John from the building?
Given:
Height of the building (h) = 50 meters
Angle of elevation (θ) = 30 degrees
To find the distance to the building (d), use the formula:
𝑑=ℎtan(𝜃)
Substitute the given values:
𝑑=50tan(30∘)
Calculate the distance using a calculator:
𝑑=50/0.577
𝑑≈86.6 meters