Lesson 28.4

Lesson 28.4 p. 39-44

Use sine, cosine, and tangent ratios.

In surveying, tangent is used to calculate distances and heights of objects. For example, if a surveyor wants to determine the height of a building, they can measure the distance from the building to their location and then use the tangent function to calculate the height.

​Uses of Tangent

1. Surveying:

Draw

You are mapping out a hiking trip to a new spot in the state park near your home. On your map, you know that you are supposed to follow a course that ends with you having moved 2.5 miles East and 3 miles South. Your map, with the start and end points, is shown.

Draw the triangle that matches the situation of this problem.

Labelling

Label with the appropriate words

Drag labels to their correct position on the image

theta

West

yes

South

East

adjacent leg

opposite leg

hypotenuse

Reorder

Put the steps in order to calculate the angle that you need to walk with respect to due East

• Identify opposite leg and adjacent leg

• Identify hypotenuse

• Determine that you will use cosine ratio

• set up cosine ratio

• use inverse cosine to find angle

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Engineers use tangent to calculate angles and distances in their designs. For instance, when designing a bridge, they need to calculate the angles of the support beams and the lengths of the cables needed to hold the bridge in place.

​

2. Engineering:

Gateway Arch in St. Louis, Missouri, is 630
feet tall. Priya can look up at a 50 degree
angle to see the top of the arch.

How far away from the base of the arch is
she standing?

In physics, tangent is used to calculate the direction and velocity of objects in motion. For example, if a ball is thrown at an angle, the tangent of that angle can be used to calculate the horizontal and vertical components of its velocity.

3. Physics:

Tangent is used in navigation to calculate the distance between two points on a map. For example, if a pilot wants to determine the distance between two ports, they can use the tangent function to calculate the distance between the two ports.

4. Navigation:

Math Response

A helicopter lifts up 1000

feet over an island and spots a swimmer that needs to be rescued.

How far away from the island is the swimmer?

Type answer here

Correct Answer: 1000

Deg^°

Rad

Work

p. 29-44