Mathematics, 10.10.2019 19:00 mostman077

In the diagram, hgf is a straight line. given ef = 4 cm and hg = gf = 3 cm, find :
(i) tan x
(ii) sin y

In the diagram, hgf is a straight line. given ef = 4 cm and hg = gf = 3 cm, find : (i) tan x

Answers: 2

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Answer from: dcox0306

If HG and GF are both 3, then the whole length of the base is 6. The tan ratio is the side opposite the reference angle (length 4) over the side adjacent to the angle (length 6), which for us looks like this:
$tan(x)= \frac{4}{6} = \frac{2}{3}=.6666667$
Now use the inverse tan button (2nd-->tan) to get
$tan^{-1} (.66667)=33.69$
As far as the sin y goes, you have to use the Law of Sines because you are not working with a right triangle in that case. I mean you are as far as having to find out what the hypotenuses are triangle EFH and triangle EFG. The hypotenuse in triangle EFH is 7.211, and the hypotenuse in triangle EFG is 5. Using the Law of Sines to solve for y, you get this:
$\frac{siny}{7.211} = \frac{sin33.69}{5}$
Solving for y and using the inverse sin gives you that y = 53.12
If you are not familiar with setting up the Law of Sines, nothing I could tell you here would help. If you are familiar, then you get the idea of where the numbers came from and why they are set up that way. Hope that helps. That second part was quite hard.

Answer from: Quest

by definition, an arc subtended by a central angle of some given measure has the same measure. so $(3x+18)^\circ=147^\circ$ .

Answer from: Quest

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w

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In the diagram, hgf is a straight line. given ef = 4 cm and hg = gf = 3 cm, find :
(i) tan x...