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A 6 foot shadow is cast by a 10 foot lamp post. What is the angle of elevation of the sun?

Sagot :

Let that be theta

  • tanØ=Perpendicular/Base

Here perpendicular is lamp post and base is the shadow

  • tanØ=10/6
  • tanØ=5/3
  • tanØ=1.67
  • Ø=59°
Semsee45idn

Answer:

59.0° (nearest tenth)

Step-by-step explanation:

This can be modeled as a right triangle (see attachment).

To find the angle of elevation (marked as [tex]x[/tex] on the attached diagram), use the tan trig ratio:

Tan trigonometric ratio

[tex]\sf\tan(\theta)=\dfrac{O}{A}[/tex]

where:

  • [tex]\theta[/tex] is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle

Given:

  • [tex]\theta = x[/tex]
  • O = 10
  • A = 6

Substitute the given values into the formula and solve for x:

[tex]\implies \sf\tan(\theta)=\dfrac{10}{6}[/tex]

[tex]\implies \sf\theta=\tan^{-1}\left(\dfrac{10}{6}\right)[/tex]

[tex]\implies \theta = \sf 59.03624...^{\circ}[/tex]

[tex]\implies \theta = \sf 59.0^{\circ}\:(nearest\:tenth)[/tex]

View image Semsee45
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