Tutor profile: Ray S.
Determine the measure of the two acute angles of a right triangle if the measure of the legs are 5cm and 8cm.
To determine the angles of a right triangle we must first decide which trig ratio to use: SohCahToa is helpful to remember: Since the legs are the opposite "o" and adjacent "a" to the acute angles we need to use Tangent "T" . Tan x = o / a It will not matter which acute angle we find first because we can use the 180 degree rule to find the other since we know the third angle is 90 (right triangle) If we use Tan x = 8 / 5 we will be finding the larger acute angle because of the inequality rule: the larger leg is opposite the larger angle Now we need a scientific calculator: Depending on the calculator use need to use the "shift" or "2nd" key to get Tan^-1 which is the inverse of Tan when solving for x. Type in Tan^-1 (8/5) (be sure in degree mode) You should get : x = 57.99 or 58 degrees Now find smaller acute angle by 180 Triangle rule: 180 - 90 - 58 = 32 degrees Thus two acute angles are: 32 and 58 degrees We can verify smaller acute angle by Tan^-1 (5/8) = 32.005 or 32 degrees
If the ratio of the angles of a triangle are 2:3:7 what are the measures of each angle? Also determine the type of triangle as classified by the angles
Angle Definition of Triangle: Measure of the 3 angles of a triangle must add to 180 degrees. Ratio does not change when we multiple all parts by same value i.e. 2:3:7=4:6:14=2x:3x:7x Now use Definition: 2x + 3x + 7x = 180 Now solve for x: 12x = 180 , thus x = 15 , this becomes our ratio multiplier Now determine angle: 2x = 30 , 3x = 45 , 7x = 105 verify: 30 + 45 + 105 = 180 , so we have found the 3 angle measures 30, 45, 105 Because one of the angles is obtuse the triangle is an OBTUSE triangle
Determine the equation of the tangent line to the curve f(x) = 2x^2 - 4x + 7 at x = 2
Tangent line need slope "m" and y-intercept "b" y = mx + b (LINEar equation) slope "m" is the 1st derivative f'(x) = 4x - 4 , at x = 2 slope = 4(2) - 4 , so m = 4 so far we have y = 4x + b, To solve for b we need to replace x and y from original f(x) , "y" f(x) or y = 2(2)^2`- 4(2) + 7 , so y = 7 , replace now: 7 = 4(2) + b , solve for b we get b = -1 Thus equation of tangent line is y = 4x - 1
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