Mathematics
marcelotrishia:

From the top of the tower 63.2 feet high, the angle of depression of the two objects situated in the same horizontal line with the base of the building, and on the same side of the tower are 31° 16’ and 48° 28’ respectively. Find the distance between the two objects.

AZ:

Hello @marcelotrishia

marcelotrishia:

Hello

AZ:

Let's first get a drawing going :)

marcelotrishia:

Okay. Thank you

AZ:

|dw:1614745307334:dw| Does this look good to you?

AZ:

The first smaller angle is 31 degrees 16 minutes The other angle includes both and is 48 degrees and 28 seconds

marcelotrishia:

AZ:

Ah, you're using the app :/

AZ:

If you can log on www.questioncove.com then you should be able to view it but if not, are you able to see this image I'm attaching

marcelotrishia:

Thank you very much

AZ:

Our angles are 31 degrees and 16 minutes and 48 degrees and 28 minutes To convert it to only degrees, we have to divide the minutes number by 60 (since there are 60 minutes in 1 degree. So for example, if we had 25 degrees and 15 minutes $$\dfrac{\text{15 minutes}}{1} \times \dfrac{\text{1 degree}}{\text{60 minutes}}$$ and we get that 15' or 15 minutes is 0.25 degrees so 25 degrees and 15 minutes is 15.25 degrees or 15.25°

marcelotrishia:

How its happen? Please can you give me solution

marcelotrishia:

Thank you

AZ:

I can't give you the solution but I can help you get to the correct answer :)

marcelotrishia:

☹️

AZ:

So for the first step, can you convert 31 degrees and 16 minutes and 48 degrees and 28 minutes into just degrees? Just divide the minutes by 60 and that will be the decimal that comes after the degrees :)

marcelotrishia:

Hmm I don't get it :(

AZ:

What is 16 / 60 =

marcelotrishia:

4/15

marcelotrishia:

0.2666

AZ:

So 31° 16' is the same as 31.0267° Similarly, what is 28 / 60 =

marcelotrishia:

:( I don't understand, sorry. Thank you.

AZ:

28 / 60 = ??

marcelotrishia:

0.433

marcelotrishia:

:(

AZ:

Good so 48° 28’ = 48.433°

AZ:

Now we have our two angles as just degrees and not degrees° minutes'

marcelotrishia:

How? :(

AZ:

Now let's look at the first triangle we have angle of 31.267 and an adjacent side of 63.2 feet

AZ:

Do you know the trigonometric functions? Which one will we use? sin? cos? tan?

marcelotrishia:

?

AZ:

Do you know how to find sin or cos of an angle?

marcelotrishia:

Thank you, sorry I didn't get it

marcelotrishia:

Bye

AZ:

AZ:

First we have to find the length of the green line and then the blue line and then we can find the answer to your question: what is the distance between the two objects that is going to be our x and we can find it by length of blue - length of green

AZ:

sin = opposite side / hypotenuse cos = adjacent side / hypotenuse tan = opposite side/ adjacent side We know the ADJACENT side and we're trying to calculate the OPPOSITE side so do we use sin? or cos? or tan?