Question

NO LINKS!!! URGENT HELP PLEASE!!!

Please help me with #20, 22, and 24

Answer 1

see the work below

Explanation:

20.) x = √32²+32² = √2048 = 45.25

y = 32(sin60) = 27.7

z = 32(cos60) = 16

22.) x = 7√3 / cos60 = 24.25 = 14√3

y = 14√3 / tan30 = 42

sin30 = 14√3 / (z+7√3)

z + 7√3 = 14√3 / sin30

z = 14√3/√sin30 - 7√3 = 36.37 = 21√3

24.) z = 18(tan30) = 10.4

h = √10.4² + 18² = √432 = 20.785

x = y

2x² = 20.785²

x = √20.785²/2 = 14.7

y = 14.7

Answer 2

Question 20:

• x = 32√2 units
• y = 16√3 units
• z = 16 units

Question 22:

• x = 14√3 units
• y = 42 units
• z = 21√3 units

Question 24:

• x = 6√6 units
• y = 6√6 units
• z = 6√3 units

Explanation:

45-45-90 triangle

A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2. Therefore, the formula for the ratio of the sides is b : b : b√2 where:

• b is each side opposite the 45 degree angles (legs).
• b√2 is the side opposite the right angle (hypotenuse).

30-60-90 triangle

A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : √3 : 2. Therefore, the formula for the ratio of the sides is c: c√3 : 2c where:

• c is the shortest side opposite the 30° angle.
• c√3 is the side opposite the 60° angle.
• 2c is the longest side (hypotenuse) opposite the right angle.

Question 20

Side x is the hypotenuse of a 45-45-90 triangle with congruent legs measuring 32 units. Therefore b = 32.

`\implies x=b√(2)=32√(2)\; \sf units`

Side y is the side opposite the 60° angle in a 30-60-90 triangle with a hypotenuse of 32 units. Therefore, 2c = 32 so c = 16.

`\implies y = c√(3)=16√(3)\; \sf units`

Side y is the side opposite the 30° angle in the same 30-60-90 triangle.

`\implies z=c = 16\; \sf units`

Question 22

Side x is the hypotenuse of a 30-60-90 triangle with the leg opposite the 30° angle measuring 7√3 units. Therefore c = 7√3.

`\implies x=2c=2 \cdot 7 √(3)=14√(3)\; \sf units`

Therefore, other leg of the same triangle (opposite the 60° angle) measures c√3 = 7√3 · √3 = 21 units.

Side y is the hypotenuse of a 30-60-90 triangle with the leg opposite the 30° angle measuring 21 units. Therefore c = 21.

`\implies y=2c=2 \cdot 21 = 42\; \sf units`

Side z is the leg of the same 30-60-90 triangle opposite the 60° angle.

`\implies z=c√(3)=21√(3)\; \sf units`

Question 24

Side z is the side opposite the 30° angle in a 30-60-90 triangle with the other leg (opposite the 60° angle) measuring 18 units. Therefore, c√3 = 18, so c = 18/√3 = 6√3 units.

`\implies z=c = 6√(3)\; \sf units`

Therefore, the hypotenuse of the same triangle measures 2c = 12√3 units.

Sides x and y are the congruent legs of a 45-45-90 triangle with hypotenuse measuring 12√3 units. Therefore b√2 = 12√3, so b = 6√6.

`\implies x=6 √(6)\; \sf units`

`\implies y=6 √(6)\; \sf units`