Special Right Triangles Practice U3L2
1. What is the value of h?
8_/2
2. What are the angle measures of the triangle?
30°, 60°, 90°
3. What is the value of x?
5_/2
4. A courtyard is shaped like a square with 250-ft-long sides.
354.6 ft
5. What is the value of x?
5_/3
6. What is the height of an equilateral triangle with sides that are 12 cm long?
10.4 cm
7. What are the angle measures of the triangle?
45°, 45°, 90°
8. What is the value of x?
4_/2
9. A ladder is leaning against a wall with the base of the ladder 6 ft away from the wall. If the ladder is 10 ft long, how tall up the wall does it reach?
8 ft
10. What is the value of x?
4_/3
1. To find the value of "h" in the given expression 8√2/2, we can simplify it by dividing both the numerator and denominator by 2, which gives us: 4√2. Therefore, the value of "h" is 4√2.
2. The triangle in question is a 30-60-90 triangle, which means it has angle measures of 30 degrees, 60 degrees, and 90 degrees.
3. Similar to the first question, we can simplify the expression 5√2/2 by dividing both the numerator and denominator by 2, resulting in 2.5√2. Hence, the value of "x" is 2.5√2.
4. If the sides of the courtyard are each 250-ft long, then the perimeter of the courtyard would be 4 times the length of one side. Therefore, the perimeter is 4 * 250 = 1000 ft.
5. We can simplify the expression 5√3/3 by dividing both the numerator and denominator by 3. This simplifies to (√3)/√3, which in turn simplifies to 1. So, the value of "x" is 1.
6. In an equilateral triangle, all three sides are of equal length. Therefore, if the sides of the triangle are 12 cm long, then the height can be found using the formula:
Height = (sqrt(3) * side length) / 2
Plugging in the given values, we get:
Height = (sqrt(3) * 12) / 2
Height = (sqrt(3) * 12) / 2
Height = (4 * sqrt(3))
Height = 4 * 1.732 (taking the square root of 3)
Height ≈ 6.928
Rounding to the nearest tenth, the height of the equilateral triangle is approximately 6.9 cm.