Question

Can you help me this please!!!And after that, can you do “ the length of side a and b please!!!

Answer 1

To solve a right triangle means to find all unknown angles and sides

From the given figure we can seeL

A right triangle ABC, where

`\begin{gathered} \angle C=90^(\circ) \\ \angle A=53^(\circ)16^(\prime) \\ AB=961\text{ m} \end{gathered}`

Since the sum of angles of a triangle is 180 degrees, then we can find angle B by subtraction angles C and A from 180

`\begin{gathered} \angle B=180-90-53^(\circ)16^(\prime) \\ \angle B=90-53^(\circ)16^(\prime) \\ \angle B=89^(\circ)60^(\prime)-53^(\circ)16^(\prime) \\ \angle B=36^(\circ)44^(\prime) \end{gathered}`

To find a and b, we will use the trigonometry ratios sine and cosine

`\begin{gathered} sinA=(opposite)/(hypotenuse) \\ sinA=(a)/(AB) \\ sin53^(\circ)16^(\prime)=(a)/(961) \end{gathered}`

By using the cross multiplication

`\begin{gathered} a=961* sin53^(\circ)16^(\prime) \\ a=770.1721392 \\ a=770\text{ m} \end{gathered}`
`\begin{gathered} cosA=(adjacent)/(hypotenuse) \\ cosA=(b)/(AB) \\ cos53^(\circ)16^(\prime)=(b)/(961) \end{gathered}`

By using the cross multiplication

`\begin{gathered} b=961* cos53^(\circ)16^(\prime) \\ b=574.7659315 \\ b=575\text{ m} \end{gathered}`