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A blind archer knew three things:
(i) her own height
(ii) the height of the target from the ground
(iii) the horizontal distance between the target and herself.

At what angle of elevation should she shoot the arrow so that she hits the target?

A. 30°
B. 45°
C. 60°
D. can't say


Sagot :

Certainly! Let's work through this problem step-by-step to determine the angle of elevation at which the archer should shoot in order to hit the target.

### Step-by-Step Solution:

1. Identify the Given Data:
- Archer's height (h₁): 1.5 meters
- Target's height (h₂): 4.5 meters
- Horizontal distance between target and archer (d): 3 meters

2. Calculate the Height Difference:
- The height difference between the archer and the target ([tex]\(\Delta h\)[/tex]):
[tex]\[ \Delta h = h_2 - h_1 \][/tex]
Substituting the given values:
[tex]\[ \Delta h = 4.5 \, \text{meters} - 1.5 \, \text{meters} = 3.0 \, \text{meters} \][/tex]

3. Use Trigonometry to Determine the Angle of Elevation:
- We employ the tangent function, which is the ratio of the opposite side (height difference) to the adjacent side (horizontal distance):
[tex]\[ \tan(\theta) = \frac{\Delta h}{d} \][/tex]
[tex]\[ \tan(\theta) = \frac{3.0 \, \text{meters}}{3 \, \text{meters}} = 1 \][/tex]

4. Calculate the Angle:
- To find the angle [tex]\(\theta\)[/tex], we take the inverse tangent (arctan) of 1:
[tex]\[ \theta = \arctan(1) \][/tex]

5. Convert from Radians to Degrees (if necessary):
- The inverse tangent of 1 is [tex]\(\frac{\pi}{4}\)[/tex] radians.
- Converting [tex]\(\frac{\pi}{4}\)[/tex] radians to degrees:
[tex]\[ \theta = 45^\circ \][/tex]

### Conclusion:

The angle of elevation at which the archer should shoot the arrow to hit the target is 45°. Therefore, the correct answer is:

(B) 45°
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