Question bank: Trigonometric Equation

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Question 1:

Medium

On a sunny day, a photographer decides to measure the height of a building using the shadows it casts. He notices that at a certain time of the day, the shadow of the building measures 10 meters and forms an angle of 60º with the ground. The photographer knows that the tangent of the angle between the shadow and the line pointing to the top of the building is equal to the height of the building divided by the length of the shadow. What would be the height of the building in meters?

Trigonometric Equation

Question 2:

Medium

Imagine you need to calculate the height of a tower. By observing its shadow and measuring the distance between you and the base of the tower, you discover that the angle formed between your vertical line and the line connecting you to the base of the tower is 60 degrees. Additionally, the distance between your vertical line and the base of the tower is 40 meters. To find the height of the tower, you need to solve the following trigonometric equation: h = d * tan(θ), where h is the height of the tower, d is the horizontal distance between the observer's vertical line and the base of the tower, and θ is the angle of inclination. What is the height of the tower?

Trigonometric Equation

Question 3:

Medium

An observation tower is 80 meters high and an observer, at the top of the tower, sights a boat at sea at an angle of depression of 30 degrees. Considering sea level as a reference, create and solve a trigonometric equation that determines the horizontal distance from the boat to the base of the tower. Use the trigonometric relations sine, cosine, and tangent to solve the equation, considering that tg(30°) = 0.5774, sin(30°) = 0.5, and cos(30°) = 0.866.

Trigonometric Equation

Theorical Question

Contextualized Question

Question 4:

Medium

Trigonometric Equation

Basic Calculus

Question 5:

Very Hard

A ladder with a length of 5 meters is leaning against the ground and a wall, forming a 60-degree angle with the ground. A painter wants to paint an area on the wall that is 4 meters high, and the base of this area is directly above the point where the ladder touches the ground. To paint this area, the painter needs to climb up to the point where the wall and the area meet. Considering the situation described, determine the height the painter must climb on the ladder to paint the desired area.

Trigonometric Equation

Contextualized Question

Calculus Question

IARA TIP

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