Introduction to trig word problems:
Greek Mathematician Ptolemy, Father of trigonometry proved the equation sin2A+cos2A=1 using geometry involving a relationship between the chords of a circle. Trigonometry was mainly concerned with establishing the relations between sides and angles of a triangle. The trigonometry consists of angles, quadrants, ratios and Identities, Compound Angles, and trigonometrical Equations. The trigonometry word example problems and practice problems are given below.
Example Problems for Trig Word Problems:
Trig word problems - Example: 1
The top of a tower was seen from the top and the bottom of a building of height 10 m at angles of elevation 45° and 60°. Determine the height of the tower.
Solution:
Let AB be the tower CD be the building of height 10 m.
Let DE be perpendicular to AB from D.
At C, the angle of elevation of A is 60°.
That is ?BCA = 60°
At D, the angle of elevation of A is 45°.
That is ?EDA = 45°
BE = CD = 10 m (since BEDC is a rectangle)
Let AE be x in metres, then AB is = x +10 m
In a right angled triangle ABC
tan60° = AB/BC (or) v3 = (x + 10m)/BC
After solve this, we get
ED = BC = (x + 10m)/v3
In a right angled triangle AED
tan45° = AE/ED (or)
v3 x = x + 10 m
v3 x – x = 10 m
x( v3 –1) = 10 m
After solving this, we get
= 5 (1.732+1)m = 5 (2.732) m = 13.66 m
Height of the tower AB = x + 10 m = 13.66 m + 10 m = 23.66 m
Trig word problems - Example: 2
Determine the length of the chord of a circle of radius 10 cm subtending at the centre the angle of 144°.
Solution:
Let AB be a chord of a circle with centre 0 of radius 10 cm. Draw OC?AB. Then C is the mid point of AB
?AOB = 144°
?COB = 72°
In right angled triangle OCB
OB/BC = sin 72°
BC = 10 sin 72° cm
= 10 × 0.9511 cm
= 9.511 cm
Length of chord AB = 2 × BC
= 2 × 9.511 cm = 19.022cm . Is this topic Translation Math hard for you? Watch out for my coming posts.
Practice for Trigonometry Word Problems:
1. A flag staff stands on the top of 6 m high tower. From a point on the ground the angle of elevation of given top of the flag staff is 60° and from the same point the angle of elevation of the top of the tower is 45°. Determine the height of the flag staff.
Answer: 4.392
2. A ladder placed that against the wall such that, the ladder are reaches the top of the wall then height 6 m and the ladder is inclined at an angle of 60°. Determine how far the ladder is from the foot of the wall.
Answer: 3.464
Greek Mathematician Ptolemy, Father of trigonometry proved the equation sin2A+cos2A=1 using geometry involving a relationship between the chords of a circle. Trigonometry was mainly concerned with establishing the relations between sides and angles of a triangle. The trigonometry consists of angles, quadrants, ratios and Identities, Compound Angles, and trigonometrical Equations. The trigonometry word example problems and practice problems are given below.
Example Problems for Trig Word Problems:
Trig word problems - Example: 1
The top of a tower was seen from the top and the bottom of a building of height 10 m at angles of elevation 45° and 60°. Determine the height of the tower.
Solution:
Let AB be the tower CD be the building of height 10 m.
Let DE be perpendicular to AB from D.
At C, the angle of elevation of A is 60°.
That is ?BCA = 60°
At D, the angle of elevation of A is 45°.
That is ?EDA = 45°
BE = CD = 10 m (since BEDC is a rectangle)
Let AE be x in metres, then AB is = x +10 m
In a right angled triangle ABC
tan60° = AB/BC (or) v3 = (x + 10m)/BC
After solve this, we get
ED = BC = (x + 10m)/v3
In a right angled triangle AED
tan45° = AE/ED (or)
v3 x = x + 10 m
v3 x – x = 10 m
x( v3 –1) = 10 m
After solving this, we get
= 5 (1.732+1)m = 5 (2.732) m = 13.66 m
Height of the tower AB = x + 10 m = 13.66 m + 10 m = 23.66 m
Trig word problems - Example: 2
Determine the length of the chord of a circle of radius 10 cm subtending at the centre the angle of 144°.
Solution:
Let AB be a chord of a circle with centre 0 of radius 10 cm. Draw OC?AB. Then C is the mid point of AB
?AOB = 144°
?COB = 72°
In right angled triangle OCB
OB/BC = sin 72°
BC = 10 sin 72° cm
= 10 × 0.9511 cm
= 9.511 cm
Length of chord AB = 2 × BC
= 2 × 9.511 cm = 19.022cm . Is this topic Translation Math hard for you? Watch out for my coming posts.
Practice for Trigonometry Word Problems:
1. A flag staff stands on the top of 6 m high tower. From a point on the ground the angle of elevation of given top of the flag staff is 60° and from the same point the angle of elevation of the top of the tower is 45°. Determine the height of the flag staff.
Answer: 4.392
2. A ladder placed that against the wall such that, the ladder are reaches the top of the wall then height 6 m and the ladder is inclined at an angle of 60°. Determine how far the ladder is from the foot of the wall.
Answer: 3.464
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