4-1 Right Triangle Trigonometry
43. BASKETBALL Both Derek and Sam are 5 feet 10 inches tall. Derek looks at a 10-foot basketball
goal with an angle of elevation of 29°, and Sam looks
at the goal with an angle of elevation of 43°. If Sam is directly in front of Derek, how far apart are the
boys standing?
Therefore, Derek and Sam are standing about 36.6
inches ≈ 3.1 feet apart.
44. PARIS A tourist on the first observation level of the
Eiffel Tower sights the Musée D’Orsay at a 1.4º
angle of depression. A tourist on the third
observation level, located 219 meters directly above
the first, sights the Musée D’Orsay at a 6.8º angle of
depression.
a. Draw a diagram to represent the situation.
b. Determine the distance between the Eiffel Tower
and the Musée D’Orsay.
SOLUTION: SOLUTION: Draw a diagram to model the situation. The vertical
distance from the boys' heads to the rim is
10(12) – [5(12) + 10] = 50 inches. Label the
horizontal distance between Sam and Derek as x and
the horizontal distance between Sam and the goal as
y.
a. Set the Musée D’Orsay as a bottom vertex of a
right triangle. Draw the 1.4° angle to the 1st level. Draw the 6.8° angle to the 3rd level, directly above the 1st level. b. Because the angles of depression from the 1st
and 3rd levels to the Musée D’Orsay are 1.4° and
6.8°, respectively, the angles of elevation from the Musée D’Orsay to the 1st and 3rd levels are also 1.4° and 6.8°, respectively.
From the smaller right triangle, you can use the
tangent function to find y.
From the larger right triangle, you can use the
tangent function to find x.
Use the tangent function to write an equation for the
smaller right triangle in terms of y.
Next, use the tangent function to write an equation
for the larger right triangle in terms of y.
Therefore, Derek and Sam are standing about 36.6
inches ≈ 3.1 feet apart.
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44. PARIS A tourist on the first observation level of the
Eiffel Tower sights the Musée D’Orsay at a 1.4º
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Set the equations that you found for each triangle
4-1 Right Triangle Trigonometry
Next, use the tangent function to write an equation
for the larger right triangle in terms of y.
Therefore, the distance between the Eiffel Tower
and the Musée D’Orsay is about 2310 meters.
45. LIGHTHOUSE Two ships are spotted from the top of a 156-foot lighthouse. The first ship is at a 27º
angle of depression, and the second ship is directly
behind the first at a 7º angle of depression.
a. Draw a diagram to represent the situation.
b. Determine the distance between the two ships.
SOLUTION: Set the equations that you found for each triangle
equal to one another and solve for x.
a. Draw two right triangle with common height and
base on the same line. The light house is 156 ft, label
the height 156. Since Ship 1 has an angle of
depression of 27°, label the angle opposite 156 ft in the smaller triangle 27°. Since Ship 2 has an angle of
depression of 7°, label the angle opposite 156 ft in the larger triangle 7°.. Therefore, the distance between the Eiffel Tower
and the Musée D’Orsay is about 2310 meters.
45. LIGHTHOUSE Two ships are spotted from the top of a 156-foot lighthouse. The first ship is at a 27º
angle of depression, and the second ship is directly
behind the first at a 7º angle of depression.
a. Draw a diagram to represent the situation.
b. Determine the distance between the two ships.
b. From the smaller right triangle, you can use the
tangent function to find x.
SOLUTION: a. Draw two right triangle with common height and
base on the same line. The light house is 156 ft, label
the height 156. Since Ship 1 has an angle of
depression of 27°, label the angle opposite 156 ft in the smaller triangle 27°. Since Ship 2 has an angle of
depression of 7°, label the angle opposite 156 ft in the larger triangle 7°.. From the larger right triangle, you can use the
tangent function to find y.
b. From the smaller right triangle, you can use the
tangent function to find x.
Therefore, the distance between the two ships is
about 964 feet.
From the larger right triangle, you can use the
tangent function to find y.
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46. MOUNT RUSHMORE The faces of the presidents at Mount Rushmore are 60 feet tall. A
visitor sees the top of George Washington’s head at
a 48º angle of elevation and his chin at a 44.76º angle
of elevation. Find the height of Mount Rushmore.
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the distance
between the two ships is
4-1 Therefore,
Right Triangle
Trigonometry
about 964 feet.
46. MOUNT RUSHMORE The faces of the presidents at Mount Rushmore are 60 feet tall. A
visitor sees the top of George Washington’s head at
a 48º angle of elevation and his chin at a 44.76º angle
of elevation. Find the height of Mount Rushmore.
SOLUTION: From the smaller triangle, you can use the tangent
function to find y.
From the larger triangle, you can use the tangent
function to find y.
Next, set the two equations equal to one another to
solve for x.
Therefore, Mount Rushmore is about 500 feet tall.
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