One of the angles of a right triangle is 30 degrees, if the hypotenuse is 8 mm, what is the area?

How to find the area of a triangle and lengths using the Pythagorean Theorem, sin, cos, tan and 30, 60 90 degree right triangle formula.
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[@obviousgiant4568]

I've been watching these videos for a few weeks now and the professor does a great job in breaking down complex explanations into easy to understand and follow instructions. Invaluable!

[@kennysimms5217]

This helps out knowing this if you're an electrician who runs conduit. For example if you need to bend a 8 inch offset in the conduit and use 30 degree bends. All you need to do is multiply your offset height by 2 to get a hypotenuse of 16 inches between bends. Of course by changing your degree changes your multiplier to get your hypotenuse.

[@devonwilson5776]

Greetings. Yes we can. The answer is 14 MM^2. If we say that angle BAC= 30 degrees, represent BC as the height, and AC as the base. We can quickly determine the value of AC by saying that Sin 30 degrees = A/8, and A=8(.5) MM= 4 MM. Now, we can use either trigonometric principles and or Pythagoras' theorem to find the remaining value, the base AC. Using Pythagoras' theorem, we have AC^2= AB^2-BC^2= 8^2-4^2=64-16=48. Now, AC equals the square root of of 48 MM. That is AC = 48^1/2= 4 times 3^1/2. Moving forward, now that we have both the base and the height of the triangle, we will use A=1/2BH to get A=1/2×4×4×3^1/2 MM^2 = 8×3^1/2 MM^2=8×1.7321 MM^2 =13.8564 MM^2= 13.9 MM^2 rounded.

[@danieldennis9831]

Sin30° is .5. Hypotenuse is 8 mm opposite side is 4 mm. cos30° multiplied by 8 mm is 6.928 so area is 13.856 approximately. (Cos30°*hyp*opp/2)

[@the_big_dog813]

That's how I did it, didn't recall the "shortcut" he used. ;)

[@mytube082007]

Used Sin(30) to get opp side; b/8 = 0.5; b=4 Then, used a^2 + 4^2 = 8^2 to get a = 4sqrt(3) Area = 1/2 × 4sqrt(3) x 4 = 8sqrt(3)

[@raya.pawley3563]

Thank you

[@russelllomando8460]

dang....got it. used trig + Pyth Theo. More fun than 30-60-90. thanks.

[@stevegreen2432]

I mixed both methods and got 2*sqrt48=approx 13.9

[@davidloewen5528]

Dang, I was hoping for a very simple refresh of Trig, lol. But 👍🏼on using a metric measurement.

[@monza1002000]

Sign Rule

[@vamsm]

For a right triangle, if there is a 30 degree angle, the length of the side opposite that angle is one-half of that of the hypotenuse.

[@michaelgonzalez7240]

I think its the sin of 30 = .5 X8 =4 then the cos of 30 = .866 X8 = 6.928 then comes 4 x 6.928 =27.712 / 2 = 13.856mm.

[@st.george007]

What is your convention on signifiacant figures?

[@vespa2860]

Random, it appears from experience (although he does tend to round down). In this example: 13.8564......... is rounded to 13.85 It should be 13.86 Is 13.8599 = 13.85 or 13.86? edit - just watched the next video on cell towers. 4.88 or 4.89? Admittedly, he normally qualifies with an estimated answer.

[@HelenMontgomery]

More of the new math

[@user-iy1vu5vx1b]

13.86 mm

[@almklit]

Is the length of side B 6.928203230275509 mm or 6.93

[@craigwebster3828]

13.86

[@olivemd]

Amazing what is still lurking in my little grey cells. Maybe starting to refresh Geometry helped?

[@user-mf1oo6ol3t]

13.86 mmsq

[@henkhu100]

Why not just flip the triangle around the base? We then have an equilateral triangel with sides of 8, so the hight of our triangle is 4. Pythagoras gives the base is 4⎷3. And the area is 8⎷3. No trig needed.

[@richardduggar4665]

8 square root of 3 mm squared

[@richardduggar4665]

Sides are x, x square root of 3, 2x😮

[@guylewis7418]

8 times square root of three?

[@JohanArnout]

If your students draw a Triangle of eight three and four mm they will find out it's pretty tiny. Measurements in centimeters would be more adequate. Probably you're not aware how small millimeters are. Why not use metrical system like the rest of the world?

[@Pd-17]

Try drawing a kilometer or mile in your notebook... It's the math that matters here, not the units. If the units are too small and you do need to draw it out. Then use a reference scale for big and small units. Also millimeters (mm) is metric.