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egoroff_w [7]
3 years ago
12

Find the measure of angle t

Mathematics
1 answer:
natima [27]3 years ago
5 0

\huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }

\large\underline{  \boxed{ \sf{✰\:Important\: point's }}}

  • ➢Given two lines are intersecting lines
  • ➢ as it's clearly known when two or more lines meet each other at a specific points is said to be as intersecting lines nd they must be having a common point
  • ➢Here angle t and angle 120⁰ forms adjacent angles
  • and sum sum of adjacent angles is 180⁰

{ \rule{70mm}{2.9pt}}

\underline{  \boxed{ \sf{✵\: let's\: solve\:✵}}}

\sf ➛\angle \: 120 \degree + \angle \:t  = 180\degree \\   \sf ➛\angle  \:t = 180 \degree -   \angle \:120 \degree \\   \sf ➛\angle \: t =  \:60 \degree

{ \rule{70mm}{2.9pt}}

\boxed{✛\underline{  \boxed{ \sf{ \: \angle \: t = 60 \degree  \: }}}✛}

Hope it helps !

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Given:

A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course.

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A short time later, the bearing to the mountain becomes 45°.

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We need to find the measure of NM.

We\text{ know that }\angle INM\text{ and }\angle\text{XNM are supplementary angles.}

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\angle INM+\angle NIM+\angle INM=180^o\text{Substitute }\angle INM=135^o\text{ and }\angle NIM=35^o\text{ in the equation.}

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Consider the sine law.

\frac{\sin N}{IM}=\frac{\sin M}{IN}=\frac{\sin I}{NM}

Take the equation to find the measure of NM.

\frac{\sin N}{IM}=\frac{\sin I}{NM}\text{Substitute }\angle N=135^o,\angle I=35^o,\text{ and IM=10 in the equation.}

\frac{\sin 135^o}{10}=\frac{\sin35^o}{NM}

NM=\frac{\sin 35^o}{\sin 135^o}\times10NM=8.11

Hence the measure of NM is 8.1 km.

The plane is 8.1 km far from the mountain when the second bearing is taken.

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