Question

extra practice

1. write an equation to find how far the bird is from the boy.

then solve the equation. round to the nearest tenth.

1. a party hat is in the shape of a cone with dimensions shown.

find the height of the hat. round to the nearest tenth.

1. larry wants to go from his house to his grandmothers house. how much distance is saved if he takes main street instead of market and exchange?
2. suppose greenville, rock hill, and columbia form a right triangle. what is the distance from columbia to greenville?

persevere with problems find the missing measure in each figure below.
round to the nearest tenth if necessary.
16.
17.
lesson 6 use the pythagorea

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\). For the party - hat (cone), the slant height \(l = 10\) in (hypotenuse of the right - triangle formed by radius \(r\) and height \(h\) of the cone), and radius \(r=4.3\) in. Let the height of the cone be \(h\). Then the equation is \(h^{2}+r^{2}=l^{2}\), substituting \(r = 4.3\) and \(l = 10\), we get \(h^{2}+4.3^{2}=10^{2}\).

Step2: Simplify the equation

First, calculate \(4.3^{2}=18.49\) and \(10^{2}=100\). So the equation becomes \(h^{2}+18.49 = 100\). Then, subtract \(18.49\) from both sides: \(h^{2}=100 - 18.49\).

Step3: Calculate the value of \(h^{2}\)

\(h^{2}=81.51\).

Step4: Solve for \(h\)

Take the square root of both sides: \(h=\sqrt{81.51}\approx9.0\) in.

Answer:

The height of the party - hat is approximately \(9.0\) in.