The breakfast club free download. Grade 10 trigonometry problems and questions with answers and solutions are presented. Crackle paint finish wood.
Unit 9 – Trigonometric Applications This unit finishes our coverage of trignometry in this e-text. This unit develops the three main formulas, the area, the Law of Sines, and the Law of Cosines, in relationship to classic right triangle trigonometry. Other Applications of Right Triangles. In general, you can use trigonometry to solve any problem that involves right triangle. The next few examples show different situations in which a right triangle can be used to find a length or a distance. Thus here we have discussed Trigonometry and its importance as every student of math is expected to know about the application of this branch of mathematics in daily life. Solve sample questions with answers and cross-check your answers with the NCERT Solutions on some applications of Trigonometry. Some applications include studying changes in the Earth's surface and managing natural hazards. How do you solve some applications of trigonometry RD sharma excersise 8.1 class 10? All answers of.
Problems
- Find x and H in the right triangle below.
Solutions to the Above Problems
- x = 10 / tan(51°) = 8.1 (2 significant digits)
H = 10 / sin(51°) = 13 (2 significant digits) - Area = (1/2)(2x)(x) = 400
Solve for x: x = 20 , 2x = 40
Pythagora's theorem: (2x)2 + (x)2 = H2
H = x √(5) = 20 √(5) - BH perpendicular to AC means that triangles ABH and HBC are right triangles. Hence
tan(39°) = 11 / AH or AH = 11 / tan(39°)
HC = 19 - AH = 19 - 11 / tan(39°)
Pythagora's theorem applied to right triangle HBC: 112 + HC2 = x2
solve for x and substitute HC: x = √ [ 112 + (19 - 11 / tan(39°))2 ]
= 12.3 (rounded to 3 significant digits) - Since angle A is right, both triangles ABC and ABD are right and therefore we can apply Pythagora's theorem.
142 = 102 + AD2 , 162 = 102 + AC2
Also x = AC - AD
= √( 162 - 102 ) - √( 142 - 102 ) = 2.69 (rounded to 3 significant digits) - Use right triangle ABC to write: tan(31°) = 6 / BC , solve: BC = 6 / tan(31°)
Use Pythagora's theorem in the right triangle BCD to write:
92 + BC2 = BD2
Solve above for BD and substitute BC: BD = √ [ 9 + ( 6 / tan(31°) )2 ]
= 13.4 (rounded to 3 significant digits) - The triangle is right and the size one of its angles is 45°; the third angle has a size 45° and therefore the triangle is right and isosceles. Let x be the length of one of the sides and H be the length of the hypotenuse.
Area = (1/2)x2 = 50 , solve for x: x = 10
We now use Pythagora to find H: x2 + x2 = H2
Solve for H: H = 10 √(2) - Let a be the length of the side opposite angle A, b the length of the side adjacent to angle A and h be the length of the hypotenuse.
tan(A) = opposite side / adjacent side = a/b = 3/4
We can say that: a = 3k and b = 4k , where k is a coefficient of proportionality. Let us find h.
Pythagora's theorem: h2 = (3k)2 + (5k)2
Solve for h: h = 5k
sin(A) = a / h = 3k / 5k = 3/5 and cos(A) = 4k / 5k = 4/5 - Let b be the length of the side opposite angle B and c the length of the side opposite angle C and h the length of the hypotenuse.
sin(B) = b/h and cos(B) = c/h
sin(B) = cos(B) means b/h = c/h which gives c = b
The two sides are equal in length means that the triangle is isosceles and angles B and C are equal in size of 45°. - The diagram below shows the rectangle with the diagonals and half one of the angles with size x.
tan(x) = 5/2.5 = 2 , x = arctan(2)
larger angle made by diagonals 2x = 2 arctan(2) = 127° (3 significant digits)
Smaller angle made by diagonals 180 - 2x = 53°. - Let x be the length of side AC. Use the cosine law
122 = 82 + x2 - 2 · 8 · x · cos(59°)
Solve the quadratic equation for x: x = 14.0 and x = - 5.7
x cannot be negative and therefore the solution is x = 14.0 (rounded to one decimal place). - The diagram below show the two buildings and the angles of depression and elevation.
tan(20°) = 200 / L
L = 200 / tan(20°)
tan(10°) = H2 / L
H2 = L × tan(10°)
= 200 × tan(10°) / tan(20°)
Height of second building = 200 + 200 × tan(10°) / tan(20°)
Trigonometry
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