if tan= 6/8, then what is sin??? (geometry)?

👨🏻‍🏫 學術台 數學
2009-04-17 4:15 pm
thankyou for your help!!
更新1:

ALSOOOOO can anyone solve the equation sin(theta)=0.3 to the nearest 10th? while using restrctions 90degrees<theta<180degrees A.theta=17.5degrees b theta=107.5degrees c.theta=162.5degrees d.theta=197.5degrees

回答 (10)

2009-04-17 4:22 pm
✔ 最佳答案
The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. This being said (from the given of the problem), the following are true

Length of opposite side = 6 units
Length of the adjacent side = 8 units

From the given, the length of the hypotenuse is determined by the Pythagorean theorem, i.e,

Hypotenuse = sqrt (6^2 + 8^2) = sqrt (100) = 10

and since the sine of an angle is the ration of the opposite side to that of the hypotenuse, then

sine of the angle = 6/10 = 3/5

Hope this helps.
👍 0 👎 0
2009-04-17 11:35 pm
tan=6/8

so solve for sin, we 1st find the other side of the right triangle which is the hypotenuse..

we use the pethagorean theorem;

c=√(a^2+b^2)
c=√(6^2+8^2)
c=√(36+64)
c=√100
c=10

so

sin(x)=opposite/hypotenuse

sin=6/10 or 3/5 answer//
👍 0 👎 0
2009-04-17 11:30 pm
the tan of any angle is the equal to the side opposide the angle divided by the side adjacent(next to) to the angle. use theorem of phytagoras to find the hypotenuse, it should be 6^2 + 8^2 = Hypotenuse^2
therefore the hypotenuse is 10
now u can find the sin of the angle, sin of an an angle is the side opposite the angle divided by the length of the hypotenuse, so it will be
Sin = 6/10

hope this helped
👍 0 👎 0
2009-04-17 11:27 pm
tanθ = 6/8 = 3/4 (3 is the vertical height of a right triangle and 4 is the base)

3^2 + 4^2 = x^2 (according to the Pythagorean theorem)
9 + 16 = x^2
25 = x^2
x = √25
x = 5 (5 is the hypotenuse of a right triangle)

∴ sinθ = 3/5
👍 0 👎 0
2009-04-17 11:26 pm
sin/sqrt(1- sin^2) = 6/8

sin^2 / (1- sin^2) = 36/64

sin^2 (1 + 36/68) = 36/64

sin ^ 2 = 36/(36 + 64) = 36/100

sin = 6/10 = 3/5

since tan is positive, the angle can be in the first quadrant, and sin can also be in the first quadrant and its sign is +ve

answer 3/5
👍 0 👎 0
2009-04-17 11:22 pm
tan x = 6 / 8 = 3 / 4
sin x = 3 / 5
👍 0 👎 0
2009-04-17 11:22 pm
I assume you mean

tan(angle) = 6/8

What this means is that we know the length of two sides of an imaginary triangle. The opposite and adjacent sides.

Opposite = 6
Adjacent = 8

Have you heard of the 3,4,5 triangle?

If opposite = 3, adjacent = 4 then hypotenuse = 5

This is just that triangle, but twice the size, giving us a hypotenuse of 10

So...

sin(angle) = opposite / hypotenuse = 6/10
👍 0 👎 0
2009-04-17 11:21 pm
That would mean you have a right triangle with legs 6 and 8.
The hypotenuse would be 10.

sin=6/10=3/5
👍 0 👎 0
2009-04-17 11:21 pm
tan = opposite / adjacent
sin = opposite / hypotenuse

because you're working with sin and tan, you can assume you have a right angled triangle. therefore, you can use a^2 + b^2 = c^2, where a and b are the sides, and c is the hypotenuse.

6^2 + 8^2 = c^2
c = sqrt (100) = 10

sin = 6/10 = 3/5
👍 0 👎 0
2009-04-17 11:20 pm
sin (theta) = 3/5

tan (theta) = 3/4 then hypotenuse = 5

sin(theta) = opposite side/ hypotenuse = 3/ 5
👍 0 👎 0


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