The diagonal of a rectangle of width 3.8, makes an angle of 32° 15' with each of the longer sides. Find the length of the diagonal, and the length of the rectangle.
Im not sure how to picture/draw the shape, which in term will tell me if it is cos, sin or tan. Also will someone explain to me what the degree and comma sign means? (after 32 and 15) Thanks in advance.
4 answers
Ok, I know how to do this question, but I just don't get the apostrophe after 15. Supposedly, it means seconds but I don't know what that has to do with this.
Suggestion:
Sketch a rectangle ABCD, with A at the topleft corner. AB as the width of 3.8 and AD as the length.
Draw the diagonal BD.
Now look at the right-angled triangle BCD
angle DBC = 32° 15'
The unit measure of and angle in common notation is the degree. There are 360° in one complete rotation, (a whole pizza)
Each degree is subdivided into 60 minutes and each minute is again divided into 60 seconds.
( I know, I know, the same units we have for time, very confusing)
so 32° 15' = 32° + 15/60° = 32.25°
You must learn the basic definitions of sine, cosine and tangent in terms of sides of a right-angled triangle.
So here
sin 32.25° = DC/BD
sin 32.25 = 3.8/BD
BD sin32.25 = 3.8
BD = 3.8/sin 32.25 <----- use your calculator
BD = 3.8/.533614515 <---- don't round off here
= 7.12124..
= appr 7.1 units
similarly , tan 32.25 = 3.8/BC
BC = ......
your turn
Sketch a rectangle ABCD, with A at the topleft corner. AB as the width of 3.8 and AD as the length.
Draw the diagonal BD.
Now look at the right-angled triangle BCD
angle DBC = 32° 15'
The unit measure of and angle in common notation is the degree. There are 360° in one complete rotation, (a whole pizza)
Each degree is subdivided into 60 minutes and each minute is again divided into 60 seconds.
( I know, I know, the same units we have for time, very confusing)
so 32° 15' = 32° + 15/60° = 32.25°
You must learn the basic definitions of sine, cosine and tangent in terms of sides of a right-angled triangle.
So here
sin 32.25° = DC/BD
sin 32.25 = 3.8/BD
BD sin32.25 = 3.8
BD = 3.8/sin 32.25 <----- use your calculator
BD = 3.8/.533614515 <---- don't round off here
= 7.12124..
= appr 7.1 units
similarly , tan 32.25 = 3.8/BC
BC = ......
your turn
From bobpursley, one of our math tutors:
It is 32.25 degrees.
The 15' is 15 minutes. 60 min per degree.
NO ONE does those anymore. They do decimals.
It is 32.25 degrees.
The 15' is 15 minutes. 60 min per degree.
NO ONE does those anymore. They do decimals.
I like 'em. People use decimals because of calculators. When I see °'" I run to my trig tables and do some interpolation!
1 answer