Question

Find the name of the person who first produces a table for solving a triangle’s length and angles.
A. William Rowan Hamilton
B. Hipparchus
C. Euclid
D. Isaac Newton

Answer 1

Hint: He was also an astronomer along with being a mathematician. He is known to have been born in Nicaea in Bithynia. He also introduced the division of a circle into ${360^o}$. He is most famous in the discovery of precession which is due to the slow change in direction of rotation of the earth


Complete step by step solution:
The name of the person who first produced a table for solving a triangle’s length and angles is Hipparchus. He created a table of chords which is equivalent to a table of value of the sine function. The explanation of the construction of the table of chords is given below:
The construction of this table is based on the facts that the chords of ${60^o}\,\,and\,\,{90^o}$ are known, that starting from chord $\theta $ we can calculate chord$({180^o} - \theta )$as shown below:

And from the chord $\theta $ we can calculate chord $\dfrac{1}{2}\theta $. The calculation of chord $\dfrac{1}{2}\theta $ goes as follows:

:

Let the angle $AOB$ be $\theta $. Place $F$ so that $CF = CB$, place $D$ so that $DOA = \dfrac{1}{2}\theta $, and place $E$ so that $DE$ is perpendicular to $AC$. Then $ACD = \dfrac{1}{2}AOD = \dfrac{1}{2}BOD = DCB$making the triangles $BCD\,\,and\,\,DCF$ congruent. Therefore$DF = BD = DA\,\,and\,\,so\,\,EA = \dfrac{1}{2}AF$. But$CF = CB = chord({180^O} - \theta )$, so we can calculate $CF$, which gives us $AF\,\,and\,EA$. Triangles $AED\,\,and\,\,ADC$are similar; therefore $\dfrac{{AD}}{{AE}} = \dfrac{{AC}}{{DA}}$,which implies that $A{D^2} = AE.AC$ and enables us to calculate $AD.AD$is chord $\dfrac{1}{2}\theta $.
We can now find the chords of ${30^o},{15^o},7{\dfrac{1}{2}^o},{45^o}\,\,and\,\,22{\dfrac{1}{2}^o}$.This gives us chord of \[{150^o},{165^o},etc.\]and eventually we have the chords of all.
Multiples of $7{\dfrac{1}{2}^o}$.

$\theta $	\[{0^o}\]	$7{\dfrac{1}{2}^o}$	${15^o}$	$22{\dfrac{1}{2}^o}$	\[{30^o}\]	\[37{\dfrac{1}{2}^o}\]	${45^o}$	$52{\dfrac{1}{2}^o}$
chord$\theta $	$0$	$450$	$897$	$1,341$	$1,779$	$2,210$	$2,631$	$3,041$

We find the chords of angle not listed and angles whole chords are not listed by linear interpolation. For example, the angle whose chord is $2,852$ is $45 + {\left( {\dfrac{{2,852 - 2,631}}{{3,041 - 2,631}} \times 7\dfrac{1}{2}} \right)^o} = {49^o}$ approximately.

Note: Sir William Rowan Hamilton was an Irish mathematician.
Euclid was a Greek mathematician commonly called “founder of Geometry” or “father of Geometry”.
Sir Isaac Newton was an English mathematician. He formulated laws of motion and universal gravitation.