professor plum is

Question

Professor Plum is standing 15 feet from a streetlamp. The light from the lamp is making his shadow 10 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 45. About how high is the streetlamp? (3 points for drawing + 3 points for correct answer= 6 points total) Draw a diagram of this word problem (use a right triangle). Let h denote the height of the lamp. Calculate h using the tangent function and your calculator

Answer 1

lamppost

|

|

| professor

| h |

| |

|___________ |________45 degree angle

15 10" shadow

In the large triangle,

tan(45) = h (tan 45 = 1)

15 + 10

So 1 = h

25

So h = 25.

Answer 2

/|

/ |

/__| STREET LAMP POST = h

PROFESSOR'S SHADOW + LAMP POST SHADOW

(NOT DRAWN TO SCALE)

The shadow-line makes a 45 degree angle with the tip of the professor's shadow to the top of the lamp post. That means the his shadow length plus his distance to the lamp post base should equal the height of the pole, since this is an isoceles right triangle. The tan(45º) = 1, so the vertical height = the horizontal length.

The professor's shadow plus his distance from the pole is 10 feet + 15 feet = 25 feet.