Basic Trig. What is angle X if HYP = 65 in and Side A is 30 in.?

Question

This would be on a right triangle Like this =
...IY\
A I.....\ HYP
...I___x\
B

I think I have the answer but since I'm studying for a final I would like to make sure I'm doing it right.

My answer is 25.5 degrees

OOPS!!!! I'm sorry Side A is 31 in!!!!!!

Answer 1

It's a good idea to establish our unknowns and givens.

We have hyp = 65, A = 30, and our unknown is angle X.
A would be considered the opposite, since it's what angle x is projecting on. So we have opposite and hypotenuse as our unknown and givens. Opposite and hypotenuse are related by sin (SOHCAHTOA); therefore,
opp = 30
hyp = 65

sin(x) = opp/hyp
sin(x) = 30/65
sin(x) = 6/13

To solve this, we take the sine inverse of both side (sometimes known as "arcsin" but also known as sin^(-1)(x) ).

x = sin^(-1) [6/13]

What you would in this case is to first make sure your calculator is in DEG (degree) mode. Your answer will get messed up if it's in RAD (radian) mode, or GRAD mode. Then calculate as normal.

Answer 2

making use of the regulation of sines, the part length opposite the sixty 5 degree perspective would be 40 seven.4, and the part length opposite the eighty degree perspective (one hundred eighty - sixty 5 - 35) would be fifty one.fifty one. chop up the triangle into 2 suitable perspective triangles. on the left part, you have a 35 degree perspective, and a hypotenuse of fifty one.fifty one. locate the backside and top: cos 35 = b / fifty one.fifty one b = 40 two.1945 sin 35 = h / fifty one.fifty one h = 29.5449 A = bh / 2 A = 623.316 Now the different triangle. you have an perspective of eighty tiers, and a hypotenuse of 30. locate b and h cos eighty = b / 30 b = 5.20945 sin eighty = h / 30 h = 29.54423 A = bh /2 A = seventy six.9546 entire A = A1 + A2 = seven hundred.2706 sq. yards.

Answer 3

If the hyperbola is 65 inches and side A is 30 inches, then by the way you have drawn this, A is the "opposite" side from the X angle, so the sine formula, sin(theta) = A/HYP
or sin(theta) = 30/65
Using microsoft excel, I get 27 degrees

Answer 4

To do this problem you need to realize you have to use sin, that is opposite/hypotenuse so you get sin(x)= 31/65, in order to do this you take the inverse sin so its sin^-1(31/65) which is 28.4846354, just remember soh cah toa and to find the angles if you have the sides use inverse hope that helps



PS: you need your calculator to be in degree mode if the asked for the angle in degrees

Answer 5

If angle X is between side B and the hypotenuse,

Sin(X) = Opposite / Hypotenuse

Sin(X) = 30 / 65

X = Inverse Sine(30 / 65)

X = 27.486 degrees or 0.480 radians (3 decimal places)

Answer 6

cos x = 31/65 = 0.4769

angle = 61.5 deg
( this is the answer if A is the side of the angle as per your sketch)

and if A is opposite yo the angle , the angle will be
90 - 61.5 = 28 .5 deg

Answer 7

arcsin 31/65 = 28.5 degrees

Answer 8

a² = b² + c²