Trigonometry Various

[lual0209]

Please could you verify if I have the following 3 questions correct:

1. 4. Use Heron's Formula to find the area (to the nearest square inch) of a triangle with sides of length 60 inches, 72 inches, and 54 inches.

s = a + b + c/2 = 60 + 72 + 54/2 = 186/2 = 93.

K = square root of s (s - a) (s - b) (s - c) = square root of 93 (93 - 60) (93 - 72) (93 - 54) = square root of 93 (33) (21) (39) = square root of 2513511 = 1585.405626 square inches = 1585 square inches.

2. A vector has a magnitude of 6.0 and a direction of 65 degrees. Write the vector in the form v = a1i + a2j. Round a1 and a2 to the nearest hundreth.

V = a1i + a2j = (sum of V cos theta) i + (sum of V sin theta) j = sum of V (cos theta i + sin theta j).

a1 = 6.0 cos 65 degrees = 2.53570957 = 2.54.

a2 = 6.0 sin 65 degrees = 5.437846722 = 5.44.

V = 2.54 i + 5.44 j.

3. Find the dot product of u = - 3 i + 2 j and v = 5 i - j.

u * v = (- 3 i + 2 j) * (5 i - j) = - 3 (5) + 2 (- 1) = - 15 - 2 = - 17.

Thank you.

 

[Loren]

Please could you verify if I have the following 3 questions correct:

1. 4. Use Heron's Formula to find the area (to the nearest square inch) of a triangle with sides of length 60 inches, 72 inches, and 54 inches.

s = a + b + c/2 = 60 + 72 + 54/2 = 186/2 = 93. <<< Should be s = (a + b + c)/2 = etc.

 

[fasteddie65]

Loren is right; your notation is very incorrect.

K = square root of [s (s - a) (s - b) (s - c)] = square root of [93 (93 - 60) (93 - 72) (93 - 54)] = square root of [93 (33) (21) (39)] = square root of 2513511 = 1585.405626... square inches ? 1585 square inches.

When writing equations, make sure you use grouping symbols; the way you wrote it you would take the square root of 93 and multiply that by 33, 21, and 39.