find the hypotenuse in a right triangle with legs a = 3 and b = 4. 55 exercise
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Find the hypotenuse in a right triangle with legs a = 3 and b = 4.
Find the hypotenuse in a right triangle with legs a = 3 and b = 4.
55
ExerciseExercise
ExerciseExerciseFind the hypotenuse in a right triangle with legs a = 3 and b = 3.
Find the hypotenuse in a right triangle with legs a = 3 and b = 3.
3 √ 23 √ 2
Find the missing side length in a right triangle with leg b = 4 and hypotenuse 4 √ 2.
Find the missing side length in a right triangle with leg b = 4 and hypotenuse 4 √ 2.
44
ExerciseExercise
Find the hypotenuse in a right triangle with legs a = 3 and b = 3 √ 3.
Find the hypotenuse in a right triangle with legs a = 3 and b = 3 √ 3.
66
ExerciseExercise
Find the missing side length in a right triangle with leg b = 5 √ 3 and hypotenuse 10.
Find the missing side length in a right triangle with leg b = 5 √ 3 and hypotenuse 10.
55
ExerciseExercise
45-45 Right Triangle45-45 Right Triangle
If each leg of a 45-45 right triangle is a units long, then the
hypotenuse is a √ 2 units long.
If each leg of a 45-45 right triangle is a units long, then the
hypotenuse is a √ 2 units long.45°45°
aa a √ 2a √ 2
45°45°aa
Find the length of the hypotenuse in the 45-45 right triangle.
Find the length of the hypotenuse in the 45-45 right triangle. 45°45°
33 xx
45°45°33
3 √ 23 √ 2
Example 1Example 1
Find the length of the legs in the 45-45 right triangle.Find the length of the legs in the 45-45 right triangle.
45°45°
aa
45°45°aa
5 √ 25 √ 2
55
Example 2Example 2
If the perimeter is 6 + 6 √ 2, what are a and c?If the perimeter is 6 + 6 √ 2, what are a and c?
45°45°
aa cc
45°45°bb
a = 3 √ 2 and c = 6a = 3 √ 2 and c = 6
ExampleExample
If the perimeter is 20, what is a?If the perimeter is 20, what is a?
45°45°
aa cc
45°45°bb
≈ 5.86≈ 5.86
ExampleExample
Are 5, 5, and 7 the sides of a 45-45 right triangle?Are 5, 5, and 7 the sides of a 45-45 right triangle?
nono
ExampleExample
30-60 Right Triangle30-60 Right Triangle
If the short leg of a 30-60 right triangle is a units long, then the long leg is a √ 3 units long and the hypotenuse is 2a units long.
If the short leg of a 30-60 right triangle is a units long, then the long leg is a √ 3 units long and the hypotenuse is 2a units long.
60°60°2a2a
a √ 3a √ 3 30°30°
aa
Find the missing lengths x and y in the triangle.Find the missing lengths x and y in the triangle.
60°60°
44xx
30°30° yy
Since a = 4, the long leg is 4 √ 3 and the hypotenuse is
2(4) = 8 units.
Since a = 4, the long leg is 4 √ 3 and the hypotenuse is
2(4) = 8 units.
Example 3Example 3
Find the short leg and hypotenuse of a 30-60 right Δ whose long leg is 6 √ 3.
Find the short leg and hypotenuse of a 30-60 right Δ whose long leg is 6 √ 3.Since the long leg of a 30-60 right triangle is a √ 3 = 6 √ 3, it follows that the short leg it a = 6. Then the hypotenuse
is 2a = 2(6) = 12.
Since the long leg of a 30-60 right triangle is a √ 3 = 6 √ 3, it follows that the short leg it a = 6. Then the hypotenuse
is 2a = 2(6) = 12.
Example 4Example 4
Find the long leg and short leg of a 30-60 right triangle whose hypotenuse is 9.
Find the long leg and short leg of a 30-60 right triangle whose hypotenuse is 9.
The hypotenuse is 2a = 9, so the short leg is a = 4.5. The
long leg is a √ 3 = 4.5 √ 3.
The hypotenuse is 2a = 9, so the short leg is a = 4.5. The
long leg is a √ 3 = 4.5 √ 3.
Example 5Example 5
If a = 1, what are b and c?If a = 1, what are b and c?
60°60°
aacc
30°30°bb
b = √ 3 and c = 2b = √ 3 and c = 2
ExampleExample
If a = 3, what is the perimeter?If a = 3, what is the perimeter?
60°60°
aacc
30°30°bb
9 + 3 √ 3 ≈ 14.29 + 3 √ 3 ≈ 14.2
ExampleExample
If the perimeter is 25, what is c?If the perimeter is 25, what is c? 60°60°
aacc
30°30°bb
10.56610.566
ExampleExample
We know that 3, 4, and 5 are the lengths of the sides of a right triangle. Are they the sides of a 30-60 right triangle?
We know that 3, 4, and 5 are the lengths of the sides of a right triangle. Are they the sides of a 30-60 right triangle?
no; 5 ≠ 2(3)no; 5 ≠ 2(3)
ExampleExample
Find the other two sides in a 30-60 right triangle with a short leg of √ 5.
Find the other two sides in a 30-60 right triangle with a short leg of √ 5.
long leg: √ 15; hypotenuse: 2 √ 5sides: 2.2, 3.9, 4.5
long leg: √ 15; hypotenuse: 2 √ 5sides: 2.2, 3.9, 4.5
ExerciseExercise
Find the other two sides in a 30-60 right triangle with a short leg of 2 √ 7.
Find the other two sides in a 30-60 right triangle with a short leg of 2 √ 7.
long leg: 2 √ 21; hypotenuse: 4 √ 7
sides: 5.3, 9.2, 10.6
long leg: 2 √ 21; hypotenuse: 4 √ 7
sides: 5.3, 9.2, 10.6
ExerciseExercise