16. + -/2 points My Notes Let S be the triangle with vertices A = (5,...
1.) Given that the perimeter of a triangle is 216. If the angles of the triangle are in the ratio 5:6:7, determine the longest side of the triangle. 2.) 4 times the sine of a certain angle is 6 times of the square of the cosine of the same angle. Find the angle in degrees if it’s in the first quadrant. 3.) Determine k so that the points A(3,8), B(-1,0), and C(k,-2) are the vertices of a right triangle with...
Do not use I=delta/S!!! Use law of cosines Here is the question: Let r be the radius of the incircle of triangle ABC on the unit sphere S. If all the angles in triangle ABC are right angles, what is the exact value of cos r? Note in spherical geometry the angles sum is>180 Using below picture (this is what we are given), we should know angle b and the angle at the perpendicular. If we find the length on...
9. [15 Points) Let C be the boundary of the triangle with vertices (1, 1), (2, 3) and (2, 1), oriented positively i.e. counterclockwise). Let F be the vector field F(1, y) = (e* + y²)i + (ry + cos y)j. Compute the line integral F. dr. 10. (15 Points) Let S be the portion of the paraboloid z = 1-rº-ythat lies on and above the plane z = 0. S is oriented by the normal directed upwards. If F...
i need help with these 3 homework problems, thank you ! Solve a Triangle Using the Law of Sincs (SSA) Ambiguous Case Suppose that the measure of angle A and the lengths of sides a and b of a triangle are given. Depending on the length of side a (shown in red) relative to the length of the altitude h, we have four different scenarios No triangle One right triangle One oblique triangle Two triangles: One acute and one obtuse...
Chapter 11, Review Exercises, Question 015 (a) Find the area of the triangle with vertices A (6,4,3), B (4,6,4), and C(11,9, 1). Enter the exact answer. Area = Edit (b) Use the result in part (a) to find the length of the altitude from vertex C to side AB. Enter the exact answer. Length ? Edit Chapter 11, Review Exercises, Question 017 Consider the points A(3,-3,2), B(4, -5,0), C(-1,-4,0), D (6,2, -3) (a) Find the volume of the parallelepiped that...
Let a and b be the lengths of the legs of a right triangle, and c be the length of the hypotenuse. Values of two of the three lengths are given. Find the third length. a 8 and b 11 Give the exact value of the third side. The length of the third side is Type an exact answer, using radicals as needed.)
(1 point) Let P = (-30, 16) be a point on the terminal side of an angle 8. Find the exact value of the ske trigonometric functions of 0. (a) sin(0) - (b) cos(@) - (c) sec() - (d) cac() - (6) tan(0) - (1) cot() -
(Total 16 marks) 9. The vertices of the triangle PQR are defined by the position vectors 3. OQ and OR = OP (a) Find PO, PR (ii) (3) (b) Show that cos RPQ = (7) (c) 0 Find sin RPQ. Hence, find the area of triangle PQR, giving your answer in the form a3 (i) (e)
Calculate the angles, side lengths and area of the triangle with vertices at the points A = (1, 2, 1), B = (4, 8, 3), C = (7, 0, −2).
Q = (0,6, -4) R= (5,-4, -5) Consider the triangle with vertices: P= (-2,0, -1) (a) Find the vectors PO, PŘ, and QŘ (b) What is the measure of the angle at P (ZQPR)? (c) What is the perimeter of the triangle APQR ? (d) What is the area of the triangle APQR? (e) Find a vector that is perpendicular to the plane containing P, Q, and R Verify that the vector you have found is perpendicular to PO (f)...