Pythagorean Theorem
Triangle ABC is a right triangle. The side AB is 4 units long. The side BC is 3 units long. How long is the side AC?
(hint: a2 + b2 = c2)
Triangle ABC is a 3,4,5 triangle or:
32 + 42 = c2
9 + 16 = c2
25 = c2
5 = c
Triangle ABC is a 46-45-90 triangle. Side AB is 4 units long. Side BC is 4 units long. How long is the side AC?
The side AC is 4√2 units long.
Triangle ABC is a right triangle. The adjacent side is x units long. The angle opposite that side is 45°. The hypotenuse, side AC, is 13 units long. What is the side AC? Round to the nearest hundredth.
The side AC is 9.19 units long.
cos45°=x/13
13cos(45)=x
9.19=x
If sin60°= 0.8660, then cos30°=
cos30°=0.8660
Triangle ABC and DEF are right triangles. Side AB is 10 units long. Side BC is 6 units long. Side DE is 5 units long. Side EF is X units long. How long is the side EF?
10/5= 2
6/2= 3
If the sides of triangle DEF are 7,11,4 what kind of triangle is it?
Triangle DEF is obtuse.
c2 > a2 + b2
112 > 42 + 72
121 > 77
Triangle DEF is a 45-45-90 triangle. Side DF is 4 units long. How long are the legs of the triangle?
The legs are 2√2 units long.
4/√2 × √2/√2= 2√2
You are standing x feet away from a lighthouse, looking at the top of the 75ft tall lighthouse at an angle of elevation from the ground of 57°. How far are you from the lighthouse? Round to the nearest hundredth.
You are 115.49 ft from the lighthouse.
tan57°= x/75
75tan(57)= x
115.49= x
If cos65°=0.4226, then sin25°=
sin25°=0.4226
Triangle ABC and DEF are similar triangles. Side AB is 12 units long. Side BC is 5 units long. Side AC is 13 units long. Side DE is 6 units long. Side EF is X units long. Side DF is Y units long. How long are the sides EF and DF?
Side EF is 2.5 units long Side DF is 6.5 units long
12/6= 2
5/2= 2.5
13/2= 6.5
If the sides of triangle ABC are 6,13,14 what kind of triangle is it?
Triangle ABC is acute.
c2 < a2 + b2
142 < 62 + 132
196 < 205
Triangle DEF is a 30-60-90 triangle. Side DE is 3√3 units long. Side EF is X units long. Side DF is 6 units long. How long is the side EF?
The side EF is 3 units long.
The adjacent side is √3 times the opposite. The hypotenuse is 2× the opposite. 6÷2= 3. Therefore side EF is 3 units long.
You are standing 36 feet away from a light post that is 85 feet tall, looking at the top at an angle of elevation of X°. What is the angle of elevation? Round to the nearest hundredth.
The angle of elevation is 22.95°
tan(x)=36/85
x=tan-136/85
x= 22.95°
Triangle BCA is a right triangle. Angle B is 68°. Angle A is 22°. Solve for angle B. Round to the nearest ten-thousandth.
cos68°=sin(90-68)
cos68°=sin22°
0.3746=0.3746
If a tree casts a 24-foot shadow at the same time that a yardstick casts a 2-foot shadow, find the height of the tree.
The tree is 36-feet tall.
3/2=x/24
2x=72
x=36ft
Triangle DEF is a right triangle. Side DE is 12 units long. Side EF is 5 units long. How long is the side DF?
The side DF is 13 units long.
122 + 52 = c2
144 + 25 = c2
169 = c2
13 = c
Triangle ABC is a 30-60-90 triangle. Side AB is 9 units long. Side BC is n units long. Side AC is 6√3 units long. How long is the side BC
The side BC is 3√3 units long.
6√3 ÷ 2= 3√3
9 ÷ √3= 3√3
Triangle DEF is a right triangle. Side DF, the hypotenuse, is 15 units long. Side DE, the adjacent side, is 12 units long. The angle of elevation is X°. What is the angle of elevation? Round to the nearest hundredth.
The angle of elevation is 38.66°
tan(x)= 12/15
x= tan-112/15
x= 38.66
Triangle EFD is a right triangle. Angle E is 75°. Angle D is 15°. Solve for angle E. Round to the nearest ten-thousandth.
cos75°=sin(90-75)
cos75°=sin15°
0.2588=0.2588
The clock tower is 110-feet tall
x/60=5.5/3
3x=330
x=110
Triangle ABC is a right triangle. Side AB is 8 units long. Side BC is 6 units long. How long is the side AC?
Triangle ABC is a 6-8-10 triangle.
Divide each number by 2 and get a 3-4-5 triangle.
Triangle DEF is a 30-60-90 triangle. Side DE is 15 units long. Side EF is x units long. Side DF is y units long. How long are sides EF and DF?
Side EF is 5√3 units long.
Side DF is 10√3 units long.
15 ÷ √3= 15√3 ÷ √3= 5√3
5√3 × 2= 10√3
You are standing on the top of an 85ft tall building looking down at a car that is 76ft away. What is the angle of depression?
The angle of depression is 41.80°
tan(x)= 76/85
x= tan-176/85
x= 41.80
Triangle ABC is a right triangle. Side AB is X units long. Side AC is 25 units long. The angle opposite is 36°. How long is the side AC? Round the nearest hundredth.
The side AB is 20.23 units long.
cos36°=x/25
26cos(36)=x
x= 20.23
A building that is 80-feet tall casts a 55-foot shadow. Your shadow is 3.5-feet long. How tall are you? Round to the nearest tenth.
You are 5.1-feet tall
80/55=x/3.5
280=55x
x=5.1