Problems with Two Right Triangles, Quiz

From two points on the same side of a tower,

20

m apart in a line with its foot, the angles of elevation of the top are

60^\circ

and

30^\circ

. How tall is the tower?

A

20\sqrt{3}

m

B

30

m

C

10\sqrt{3}

m

D

10

m

From the top of a

50

m tower, the angles of depression of two cars on opposite sides are

30^\circ

and

60^\circ

. How far apart are the cars?

A

100

m

B

50\sqrt{3}

m

C

\displaystyle \dfrac{100}{\sqrt{3}}

m

D

\displaystyle \dfrac{200}{\sqrt{3}}

m

A flagstaff stands on a building. From a point

30

m from the base, the elevations of the top of the building and of the flagstaff are

45^\circ

and

60^\circ

. How long is the flagstaff?

A

30

m

B

30(\sqrt{3} - 1)

m

C

30\sqrt{3}

m

D

30(\sqrt{3} + 1)

m

In a two-triangle problem, what is the best habit when two right triangles share a side?

A Use only the triangle with the larger angle

B Average the two angles

C Add the two angles and use one triangle

D Write that shared side from each triangle and equate the two expressions

From the top of a

20

m building, the angle of elevation of a taller tower's top is

45^\circ

and the angle of depression of its foot is

30^\circ

. How far apart are the building and tower?

A

20\sqrt{3}

m

B

\displaystyle \dfrac{20}{\sqrt{3}}

m

C

20

m

D

40

m

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Problems with Two Right Triangles, Quiz

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