Area of a right triangle= ? One angle 17 degrees, hypotenuse 12

The simplest, most straightforward, means of solving is to multiply the hypotenuse (12) by sin(17), multiply the hypotenuse by cos(17), then multiply the aforementioned results together, and finally divide by 2. The result is approximately 20, which is what many of the other comments herein had as an answer.

As long as we are using trig anyway, just get the length of the other side as 12cos(17), easier to me

Area = (1/2)(base)(height) = (1/2)(12cos[17])(12sin[17]) = (1/2)(144)(cos[17])(sin[17]) = (1/2)(72)(2)(cos[17])(sin[17]), but sin(2x) = 2sin(x)cos(x) = (1/2)(72)sin(34) = 20.13094453... (approx 20.131 units^2)

Like others have said why not use the cosine to find the other side Unless the point was to teach the pathygorian theory. I think it's better to stick to one topic

Why couldn’t I have had a math teacher like you when I was in School to have the patience as you do and be able to dumb it down to as to absorb so easily. Thanks

This is easy. Everyone knows that sin theta = opposite side/hypoteneuse. Since theta = 17 dgrees, sin17 = opposite/ 12. Opposite side = sin 17 degrees * 12 = 3.508; cos theta = adjacent / hypotoneuse. cos17 = adjacent/12. adjacent side = cos17 *12 =5.8. So, area of triangle = .5*b*h. So, area of this triangle = .5 *cos17*sin17*(12)^2 =20.17 units^2

Like others, I'm surprised you went with Pythagoras for this. If you can do 12 sin 17° then you can do 12 cos 17° just as easily, and now you have base and height. So the area is: ½ × (12 sin 17°) × (12 cos 17°) = 72(sin 17°)(cos 17°) From the thumbnail, I thought the point of this video was going to be too teach the trig identity (which i had to look up just now) that (sin X)(cos X) = ½ sin (2X), so here we're just doing 36 × sin 34°. That seems a much cleaner way to get to the answer.

Your videos are a godsend. Thank you so much 👍

WOW...got it 20.1 SOHCAHTOA and Pythag thanks for the fun

The way I did ot is system of equation which is 12=square root of x²+y² then inverse tan(x/y)=17 this is a picture of a 12 radius circle with a line through it in which where the line touchs the edge of the circle the missing sides are the x and y that make the line intersection. This came to me naturally in thought, a interesting way to find the sides of a right angle with hypotnuse and one angle using algebra. In which you do a simpe area formula 1/2×11.47×3.508=20.1309.....

A trig question: Sin 17° = a/12 a = 12(Sin17) = 12(0.2924) = 3.5085 b =? tan17° = a/b b = a/tan17 = 3.5085/(0 3057) = 11.4758 Area triangle: A = (1/2)b×h Here b = b = 11.4758 h = a = 3.5085 A=(1/2)(11.4758)(3.5085) =(1/2)(40.2628) =20.1314 units^2 Verify... 11.4758^2+3.5084^2=?17^2 131.6940+12.3089=?289 144.0029=❌️289❌️ ?? = 12^2. Not. =17^2

thank you, teach. good review. Thanks again.

Due to your round off error, in an application of trig in a real world machine shop, your answer is off by 0.004 thousandths and by 0.0039 ten thousandths depending on the called out +/- tolerance, which is about the thinkness of a piece of copy paper or average human hair. It all depends on round off error

First thing first, from the image, we can elicit all the angles measuse as it is a right triangle so there must be one 90 degree angle which is marked in the right bottom, then addressed 17degree angle. From prior knowledge we know, triangle consist of 180 degree, so the top angle should be 180-(90+17)=73 degrees. Now, apply soh-cah-toa over this right triangle to find out the side lengths first then, we will conclude it to the area of this rectangle. apply soh at 17 degree angle, => sin 17 = x(which is vertical side length or height)/12(hypotenuse) =>12 sin 17 = x => x = 3.508 which is similar to 3.51 its time to find out the base value as we don't know, apply 'toa' criterion, tan 73 = y(base length)/3.51 =>y = 3.51 tan 73 => y = 11.48 As we find out base and height of this triangle, so now we can place it in the triangle area formula, (1/2)*x*y =0.5*3.51*11.48 =20.15

72 sin(17) cos (17)

(12*cos(17))×(12×sin(17)/2=20.130 is the answer

I cheated. I did a quick Pythagorean based upon 144 no calculator. 11.5 X 3.5 worked,, so my guesstimate was 20 square inches area. I LIKED your explanation of sin. A LOT.

I come up with approximately 20.13094453 square cubits. (Because he didn't say inches or feet.)

Loving the creativity in this video!

I got 20.08 does it still count ?!!