Question

SOMEONE PLEASE HELP ASAP!!!! Solve the triangle round to the nearest tenth.

Answer 1

s = 13.6

m∠T = 35.7°

m∠U = 61.3°

Explanation:

• Solving for side s:

To find the length of side s, we have to use the cosine rule:

`\boxed{a^2 = b^2 + c^2 - 2bc \ cosA}`,

where:

• a = unknown side
• b, c = adjacent sides
• A = angle opposite to the unknown side.

In this case, the unknown side is s, and the sides adjacent to it have lengths of 8 and 2. The angle opposite to s is ∠S = 83°. Therefore,

`s^2 = 8^2 + 12^2 -2(8)(12) \cdot cos(83^(\circ))`

⇒
`s = \sqrt{8^2 + 12^2 -2(8)(12)\cdot cos(83^(\circ))}`

⇒
`s = \bf 13.6`

• Solving for m∠T:

In order to find m∠T, we can use the sine rule:

`\boxed{(sinA)/(a)= (sinB)/(b) =(sinC)/(c)}`,

which means that the ratios of the sines of angles and their opposite sides are equal for a triangle.

The side opposite to ∠T is US = 8. Therefore:

`{(sinT)/(8) = (sin(83^(\circ)))/(13.6)}`

⇒
`sinT= (sin(83^(\circ)))/(13.6) * 8`

⇒
`T = sin^(-1)( (sin(83^(\circ)))/(13.6) * 8)`

⇒
`T = \bf 35.7^(\circ)`

• Solving for m∠U:

Now that we know the values of two angles of the triangle, we can calculate the third angle using the fact that the angles in a triangle add up to 180°:

∠U + ∠S ∠T = 180°

⇒ ∠U + 83° + 35.7° = 180°

⇒ ∠U = 180° - 83° - 35.7°

⇒ ∠U = 61.3°