A point H is 20m away from the foot of a tower on the same horizontal ground. From the point H, the angle of elevation of the point (P) on the tower and the top(T) of the tower are 30° and 50° respectively. ( a) draw a diagram to illustrate the information above.
(b) calculate correct to 3 s. f,
( I) /PT/
(ii) the distance between H and the too of the tower.
(III) the position of H if the angle of depression of H from the too of the tower is to be 40°

a. See Attachment 1

b.

c.

d.

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;

Multiply both sides by 20

Calculating OP;

We have to consider angle 30, distance OH and distance OP

The relationship between these parameters is;

Multiply both sides by 20

(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

Substitute 20 for OH and

Take Square Root of both sides

(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;

Multiply both sides by OT

Substitute

(Approximated)

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!