Answer:
Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft
Step-by-step explanation:
The illustration form a triangle that can be demarcated into 2 right angle triangle. One triangle representing depression triangle and the other elevation triangle.
Depression triangle
The opposite side of the triangle formed is the length of the pole from the base to the horizontal line of sight. Therefore,
using tangential ratio
tan 35° = opposite/adjacent
tan 35° = a/8
cross multiply
a = 8 tan 35°
a = 8 × 0.70020753821
a = 5.60166030568
a = 5.602 ft
Elevation triangle
The opposite side of this right angle triangle represent the length from the horizontal line of sight to the top of the lamppost.
tan 20° = opposite/adjacent
tan 20° = b/8
cross multiply
b = 8 tan 20°
b = 8 × 0.36397023426
b = 2.91176187413
b = 2.912 ft
Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft
Answer:
Step-by-step explanation:
If two polygons are similar, then corresponding sides are in proportion.
The corresponding sides:
4 → x
y → 15
3 → w
2 → 6
z → 9
therefore:
<em>cross multiply</em>
<em>divide both sides by 6</em>
When we draw a circle with the centre at D and have a tangent HF to the circle D at point E, the angle DEF will be a right angle.
In other words angle DEF = 90 degrees
Since HF, the tangent, is a straight line, the other angle DEH should also be = 90 degrees because the straight line has an angle of 180 degrees
Therefore angle DEF = angle DEH = 90 degrees
Therefore, angle DEF is congruent to angle DEH (Option A)
The correct answer is
<span>D. The number of degrees in its supplement
The size of the sides and the rotation is irrelevant and would still keep the angle having the same size. The number of degrees in the supplement decides how big an angle is because the larger the supplementary angle the smaller the angle we're observing will be, and vice versa.</span>
A) 42x-12
6*7=42. 6*2=12
b) 21y
11+4+6=21
