In the diagram shown,\(PT=QT=QR\)

Also,\(RT=RS\) and \(\angle PTQ=36°\)

What is \(\angle PTS\)?

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Q:

In the diagram shown,\(PT=QT=QR\)

Also,\(RT=RS\) and \(\angle PTQ=36°\)

What is \(\angle PTS\)?

Q:

This is an observation tower out in Blowing Rock, NC that is 40 feet tall. If you climb to the top and view someone's campfire at an angle of depression of 3 degrees, how far from the base of the tower is the campfire?

Round your answer to the nearest foot.

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\(\mathrm{ABCD}\) is a quadrilateral.\(\mathrm{AB}=7\mathrm{cm}\), \(\mathrm{BC}=5\mathrm{cm}\), \(\mathrm{BC}=11\mathrm{cm}\), \(\mathrm{AD}=10\mathrm{cm}\), angle \(\mathrm{BAD}=130^{\circ}\). Work out the size of angle \(\mathrm{BCD}\).

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In \(\triangle\mathrm{STU}\), the measure of \(\angle\mathrm{U}=90^{\circ},\) \(\mathrm{US}=5.9\) feet, and \(\mathrm{TU}=2.6\) feet. Find the measure of \(\angle\mathrm{T}\) to the nearest tenth of a degree.

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Solve the following problems and show your solution.

1. The angle of elevation to the top of a flagpole is \(40^{\circ}\) from a point \(30\) m away from the base of the pole. How high is the flagpole to the nearest meter?

2. How high is the building whose horizontal shadow is \(60\) m when the angle of elevation of the sun is \(58^{\circ}12^{\prime}\)? Give the answer to the nearest hundredths.

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If you place a \(38\)-foot ladder against the top of a \(32\)-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.

Q:

In \(\triangle\mathrm{NOP}\), the measure of \(\angle\mathrm{P}=90^{\circ}\), \(\mathrm{PN}=1.1\), and \(\mathrm{NO}=3.3\) feet. Find the measure of \(\angle\mathrm{N}\) to the nearest degree.

Q:

4. You are standing on the Skydeck at Willis Tower in Chicago, 1353 feet high. You look to the southeast at an angle of depression of 10° and see Soldier Field. How far away from Willis Tower is Soldier Field? Sketch a diagram and show all work.

Q:

A sun casts a shadow of a \(50\)-foot building. If the angle of elevation to the sun is \(64^{\circ}\), how long is the shadow? Round to the nearest tenth.

\(24.4 \)feet

\(114.0\) feet

\(102.5\) feet

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In the triangle \(\mathrm{ABC}\), \(\mathrm{C}=90\), \(\mathrm{AC}=3.2\mathrm{m}\) and \(\mathrm{BC}=4.8\mathrm{m}\). Find \(\mathrm{B}\).

Q:

In \(\triangle\mathrm{MNO}\), the measure of \(\angle\mathrm{O}=90^{\circ}\), \(\mathrm{ON}=35\), \(\mathrm{NM}=37\), and \(\mathrm{MO}=12\). What is the value of the tangent of \(\angle\mathrm{M}\) to the nearest hundredth?

Q:

When a coordinate grid is superimposed on a map of Lanesville, the middle school is located at \((15, 23)\) and the library is located at \((27, 9)\). If each unit represents \(1\) mile,, how many miles apart are the middle school and the library? Round your answer to the nearest tenth.

Q:

From the top of a building \(21\) m tall, the angle of depression to a car on the road below is \(70\) degrees. How far is the car from the base of the building? Sketch a diagram to help you...

a. \(61\) m

b. \(57.7\) m

c. \(7.6\) m

d. \(19.7\) m

Q:

The maximum slope of a wheelchair ramp is \(1:12\). For a wheelchair ramp made with these specifications, what angles does the ramp make with the ground? Round your answer to the nearest hundredth.