Geometry: MIXED

The line represented by the equation 6x − 2y = 14 is transformed by a dilation centered at (2,-1) with a scale factor of 2. The image of the line is…

the original line

In the diagram below, ERM~JTM. Which statement is not always true?

CosT = RM/EM

Which of the following ratios is equivalent to sin D?

Sin D = FE/ED

In right triangle JOE, hypotenuse JO = 31.8 and m∠J = 38°. To the nearest tenth, determine the length of EJ.

25.1

X = ___

x=2.8

The Washington Monument, shown below, is in Washington, D.C. At a point on the ground 200 feet from the center of the base of the monument, the angle of elevation to the top of the monument is 70.19°.

What is the height of the monument, to the nearest foot?

555 feet

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 24 feet up. The ladder makes an angle of 73∘ with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

25.1 feet

From the observation deck of a skyscraper, Isabella measures a 45∘ angle of depression to a ship in the harbor below. If the observation deck is 1036 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.

1036 feet

The ramp shown in the diagram below has an angle of elevation of 4.8º. The ramp is built to a landing 0.6 m above the ground.

Determine and state the length of the ramp, to the nearest tenth of a meter.

7.2

A boat heading out to sea starts out at Point A, at a horizontal distance of 649 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light to be 5∘. At some later time, the crew measures the angle of elevation from point B to be 2∘. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.