Question

Help on solving these special right triangle problems??

Look at picture

Thank you!!

Answer 1

A 30°- 60°- 90° triangle has corresponding sides of: b - b√3 - 2b

The sides are OPPOSITE of the angle (the side the angle is not touching)

4. Answer:
`\bold{x = 7,\quad y=(7\sqrt3)/(3)}`

Explanation:

`90^o: 2b = (14\sqrt3)/(3)\\\\\\30^o: b=y\\\\.\quad (1)/(2)\cdot (14\sqrt3)/(3)=y\\\\.\quad (7\sqrt3)/(3)=y\\\\\\60^o: b\sqrt3=x\\\\.\quad \bigg((7\sqrt3)/(3)\bigg)\sqrt3=x\\\\.\quad (7\cdot 3)/(3)=x\\\\.\quad 7=x\\`

5. Answer:
`\bold{x=(10\sqrt3)/(3),\quad y=(5\sqrt3)/(3)}`

Explanation:

`60^o: b\sqrt3=5\\\\30^o:b=y\\\\.\qquad (5)/(\sqrt3)=y\\\\\\.\qquad (5)/(\sqrt3)\bigg((\sqrt3)/(\sqrt3)\bigg)=y\\\\\\.\qquad (5\sqrt3)/(3)=y\\\\\\90^o: 2b=x\\\\\\.\qquad 2\bigg((5\sqrt3)/(3)\bigg)=x\\\\\\.\qquad (10\sqrt3)/(3)=x`

Answer 2

Figure 4 ⇒ x =
`(10√(3))/(3)` = 5.774

y =
`(5√(3))/(3)` = 2.887

Figure 5 ⇒ x = 7

y =
`(7√(3) )/(3)` = 4.041

Explanation:

Figure 4:

∵ The Δ is right triangle

∴ Use trigonometry function

∵ 5/x = sin(60°)

∴ x = 5/sin(60°) =
`(10√(3) )/(3)` = 5.774

∵ 5/y = tan(60°)

∴ y = 5/tan(60°) =
`(5√(3))/(3)` = 2.887

Figure 5:

∵ The Δ is right triangle

∴ Use trigonometry function

∵
`(x)/((14√(3))/(3))` = sin(60°)

∴ x =
`(14√(3))/(3)`×sin(60°) = 7

∵
`(y)/((14√(3))/(3))` = cox(60°)

∴ y =
`(14√(3))/(3)`×cos(60°)=
`(7√(3))/(3)` = 4.041