a person is standing 12m away from a street light that is 9m tall. How tall is he if his shadow is 3m long?
Let h be the height
Using similar triangles,
h/9 = 3/15 = 1/5
h = 9/5 = 1.8m
If the measure of ÐDAB = 50°, and ÐDAC = 20°, what is ÐCAB?
To determine how tall the person is, we can use similar triangles. Here's how we can solve it step by step:
1. Draw a diagram: Draw a vertical line representing the streetlight. Label its height as 9m. Draw another line representing the person standing 12m away from the streetlight, creating a shadow.
2. Identify the similar triangles: In the diagram, there are two triangles formed, one by the person's height, shadow, and the line connecting the top of the person's head to the streetlight, and the other by the streetlight's height, shadow, and the line connecting the top of the streetlight to the person's shadow.
3. Set up a proportion: Since the triangles are similar, the ratios of corresponding sides will be equal. We can set up the proportion as follows:
(Height of person)/(Length of person's shadow) = (Height of streetlight)/(Length of streetlight's shadow)
Let's substitute the given values into the proportion:
h/3 = 9/12
Simplify the ratio:
h/3 = 3/4
4. Solve the proportion: Cross multiply and solve for h:
4h = 3 * 3
Multiply the values on the right side:
4h = 9
Divide both sides by 4:
h = 9/4
5. Calculate the height of the person: Divide 9 by 4:
h = 2.25
Therefore, the person's height is 2.25 meters.