MATH HONORS 2: A Few Triangle Trigonometry Problems
Round your answers to 3 significant figures in #1, #2, and #3, but give exact answers in #4.
1. There are various published versions of the Bermuda triangle, but one common definition is the
triangle which has its vertices located at Miami (Florida), San Juan (Puerto Rico), and the island
of Bermuda. The distance between Miami and San Juan is 1622 km. The distance between San
Juan and Bermuda is 1542 km. The distance between Bermuda and Miami is 1668 km. In
square kilometers, what is the area contained by the Bermuda Triangle?
2. Ahmed is standing at the edge of a cliff that is 82 meters above the level of the sea. He can see
a boat at an angle of depression of 4.2 degrees that is sailing towards him. Half an hour later,
the boat is still sailing towards him but is now at an angle of depression of 21.6 degrees. What is
the speed of the boat in kilometers per hour?
3. Bella needs to build a ramp at an angle of 15 degrees. She already has a strut that is 1.7 meters
long which will hold up the high end of the ramp, and the ramp itself that is 6.5 meters. How far
from the base of the ramp will she have to anchor the base of the strut?
4. (a) Special Triangle A is an isosceles right triangle.
i. What are the measures of the acute angles in Special Triangle A?
ii. Give the three basic trigonometric ratios of one of the acute angles in Special Triangle A.
(b) Special Triangle B is a right triangle whose hypotenuse is twice the length of one of its legs.
i. What are the measures of the acute angles in Special Triangle B?
ii. Give the three basic trigonometric ratios of both of the acute angles in Special Triangle B.
ANSWERS:
1.
2.
3.
4.
1 120 000 km2
1.82 km/h
6.52 m or 6.03 m
(a) i. 45o – 45o – 90o
ii. sin 45 
1
1
, cos 45 
, tan 45  1
2
2
(b) i. 30o – 60o – 90o
ii. sin 30 
1
1
3
3
1
, cos 30 
, tan 30 
and sin 60 
, cos 60  , tan 60  3
2
2
2
2
3