Problem preview

G-MG.3 Warmup M3-041-A09-V04

Use geometric methods to solve design problems under constraints such as cost, space, or ratios.

Solve a right-triangle design dimension to stated precision

Problem

A \(12\text{-}\text{ft}\) beam makes a \(60°\) angle with the ground. Use the diagram to identify the relevant sides, write a trigonometric equation, and find horizontal distance \(d\) to \(\text{two}~\text{decimal}~\text{places}\).

Answer choices

Choose your path.

Preview only

Treat d as opposite 60 degrees, so sin(60 degrees)=d/12 and d=12sin(60 degrees)=10.39 feet.

The distance d is adjacent to 60 degrees and 12 feet is the hypotenuse, so cos(60 degrees)=d/12 and d=12cos(60 degrees)=6.00 feet.

Use cos(60)=d/12 in radian mode, so d=12cos(60 radians)=-11.43 feet.

Put d in the denominator, so cos(60 degrees)=12/d and d=12/cos(60 degrees)=24.00 feet.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Inside Gozunta

More than a preview

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now

Curriculum context

Course: Math III
Standard: G-MG.3
Category: Geometry
Domain: Modeling with Geometry
Objective: Use geometric methods to solve design problems under constraints such as cost, space, or ratios.
Problem type: Solve a right-triangle design dimension to stated precision