Answer:
a. See Attachment 1
b. [tex]PT = 12.3\ m[/tex]
c. [tex]HT = 31.1\ m[/tex]
d. [tex]OH = 28.4\ m[/tex]
Step-by-step explanation:
Calculating PT
To calculate PT, we need to get distance OT and OP
Calculating OT;
We have to consider angle 50, distance OH and distance OT
The relationship between these parameters is;
[tex]tan50 = \frac{OT}{20}[/tex]
Multiply both sides by 20
[tex]20 * tan50 = \frac{OT}{20} * 20[/tex]
[tex]20 * tan50 = OT[/tex]
[tex]20 * 1.1918 = OT[/tex]
[tex]23.836 = OT[/tex]
[tex]OT = 23.836[/tex]
Calculating OP;
We have to consider angle 30, distance OH and distance OP
The relationship between these parameters is;
[tex]tan30 = \frac{OP}{20}[/tex]
Multiply both sides by 20
[tex]20 * tan30 = \frac{OP}{20} * 20[/tex]
[tex]20 * tan30 = OP[/tex]
[tex]20 * 0.5774= OP[/tex]
[tex]11.548 = OP[/tex]
[tex]OP = 11.548[/tex]
[tex]PT = OT - OP[/tex]
[tex]PT = 23.836 - 11.548[/tex]
[tex]PT = 12.288[/tex]
[tex]PT = 12.3\ m[/tex] (Approximated)
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Calculating the distance between H and the top of the tower
This is represented by HT
HT can be calculated using Pythagoras theorem
[tex]HT^2 = OT^2 + OH^2[/tex]
Substitute 20 for OH and [tex]OT = 23.836[/tex]
[tex]HT^2 = 20^2 + 23.836^2[/tex]
[tex]HT^2 = 400 + 568.154896[/tex]
[tex]HT^2 = 968.154896[/tex]
Take Square Root of both sides
[tex]HT = \sqrt{968.154896}[/tex]
[tex]HT = 31.1\ m[/tex] (Approximated)
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Calculating the position of H
This is represented by OH
See Attachment 2
We have to consider angle 50, distance OH and distance OT
The relationship between these parameters is;
[tex]tan50 = \frac{OH}{OT}[/tex]
Multiply both sides by OT
[tex]OT * tan50 = \frac{OH}{OT} * OT[/tex]
[tex]OT * tan50 = {OH[/tex]
[tex]OT * 1.1918 = OH[/tex]
Substitute [tex]OT = 23.836[/tex]
[tex]23.836 * 1.1918 = OH[/tex]
[tex]28.4= OH[/tex]
[tex]OH = 28.4\ m[/tex] (Approximated)
